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Arkiv for Matematik, 2013, Volume 52
ISSN:
0004-2080 (Print)
1871-2487 (Online)
In this volume (20 articles)
Issue 1
[1] Parallel mean curvature surfaces in symmetric spaces
Maria João Ferreira Departamento de Matemática Faculdade de Ciências, Universidade de Lisboa Renato Tribuzy Departamento de Matemática, Universidade Federal do Amazonas
Symplectic Geometry mathscidoc:1701.34002
Arkiv for Matematik, 52, (1), 93-98, 2012.3
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[2] Bad boundary behavior in star-invariant subspaces I
Andreas Hartmann Institut de Mathématiques de Bordeaux, Université de Bordeaux William T. Ross Department of Mathematics and Computer Science, University of Richmond
Spectral Theory and Operator Algebra mathscidoc:1701.32005
Arkiv for Matematik, 52, (1), 113-134, 2012.2
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We discuss the boundary behavior of functions in star-invariant subspaces ($BH$^{2})^{⊥}, where$B$is a Blaschke product. Extending some results of Ahern and Clark, we are particularly interested in the growth rates of functions at points of the spectrum of$B$where$B$does not admit a derivative in the sense of Carathéodory.
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[3] Irreducible Harish-Chandra modules over extended Witt algebras
Xiangqian Guo Department of Mathematics, Zhengzhou University Genqiang Liu College of Mathematics and Information Science, Henan University Kaiming Zhao Department of Mathematics, Wilfrid Laurier University
Rings and Algebras mathscidoc:1701.31003
Arkiv for Matematik, 52, (1), 99-112, 2012.5
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Let$d$be a positive integer, $A={\mathbb{C}} [t_{1}^{\pm1},\ldots ,t_{d}^{\pm1}]$ be the Laurent polynomial algebra, and $W=\operatorname{Der} (A)$ be the derivation Lie algebra of$A$. Then we have the semidirect product Lie algebra$W$⋉$A$which we call the extended Witt algebra of rank$d$. In this paper, we classify all irreducible Harish-Chandra modules over$W$⋉$A$with nontrivial action of$A$.
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[4] Tangential touch between the free and the fixed boundary in a semilinear free boundary problem in two dimensions
Mahmoudreza Bazarganzadeh Department of Mathematics, Uppsala University Erik Lindgren Department of Mathematics, Norwegian University of Science and Technology
Differential Geometry Metric Geometry mathscidoc:1701.10013
Arkiv for Matematik, 52, (1), 21-42, 2012.2
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We study minimizers of the functionalwhere $B_{1}^{{\mathchoice {\raise .17ex\hbox {$\scriptstyle +$}} {\raise .17ex\hbox {$\scriptstyle +$}} {\raise .1ex\hbox {$\scriptscriptstyle +$}} {\scriptscriptstyle +}}}=\{x\in B_{1}: x_{1}>0\}$ ,$u$=0 on {$x$∈$B$_{1}:$x$_{1}=0}, $\lambda^{{\mathchoice {\raise .17ex\hbox {$\scriptstyle \pm $}} {\raise .17ex\hbox {$\scriptstyle \pm $}} {\raise .1ex\hbox {$\scriptscriptstyle \pm $}} {\scriptscriptstyle \pm }}}$ are two positive constants and 0<$p$<1. In two dimensions, we prove that the free boundary is a uniform$C$^{1}graph up to the flat part of the fixed boundary and also that two-phase points cannot occur on this part of the fixed boundary. Here, the free boundary refers to the union of the boundaries of the sets {$x$:±$u$($x$)>0}.
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[5] Banach analytic sets and a non-linear version of the Levi extension theorem
Sergey Ivashkovich UFR de Mathématiques, Université de Lille-1
Complex Variables and Complex Analysis mathscidoc:1701.08011
Arkiv for Matematik, 52, (1), 149-173, 2012.4
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We prove a certain non-linear version of the Levi extension theorem for meromorphic functions. This means that the meromorphic function in question is supposed to be extendable along a sequence of complex curves, which are arbitrary, not necessarily straight lines. Moreover, these curves are not supposed to belong to any finite-dimensional analytic family. The conclusion of our theorem is that nevertheless the function in question meromorphically extends along an (infinite-dimensional) analytic family of complex curves and its domain of existence is a pinched domain filled in by this analytic family.
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[6] The Chern–Osserman inequality for minimal surfaces in a Cartan–Hadamard manifold with strictly negative sectional curvatures
Antonio Esteve Instituto de Enseñanza Secundaria Alfonso VIII Departamento de Análisis Económico y Finanzas, Universidad de Castilla-La Mancha Vicente Palmer Department of Mathematics Institute of New Imaging Technologies, Universitat Jaume I
Differential Geometry mathscidoc:1701.10014
Arkiv for Matematik, 52, (1), 61-92, 2012.5
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We state and prove a Chern–Osserman-type inequality in terms of the volume growth for minimal surfaces$S$which have finite total extrinsic curvature and are properly immersed in a Cartan–Hadamard manifold$N$with sectional curvatures bounded from above by a negative quantity$K$_{$N$}≤$b$<0 and such that they are not too curved (on average) with respect to the hyperbolic space with constant sectional curvature given by the upper bound$b$. We also prove the same Chern–Osserman-type inequality for minimal surfaces with finite total extrinsic curvature and properly immersed in an asymptotically hyperbolic Cartan–Hadamard manifold$N$with sectional curvatures bounded from above by a negative quantity$K$_{$N$}≤$b$<0.
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[7] Monomial ideals whose depth function has any given number of strict local maxima
Somayeh Bandari Department of Mathematics, Az-Zahra University Jürgen Herzog Fachbereich Mathematik, Universität Duisburg-Essen Takayuki Hibi Department of Pure and Applied Mathematics Graduate School of Information Science and Technology, Osaka University
Arithmetic Geometry and Commutative Algebra Rings and Algebras mathscidoc:1701.07001
Arkiv for Matematik, 52, (1), 11-19, 2012.5
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Herzog J, Qureshi A A. Persistence and stability properties of powers of ideals[J]. Journal of Pure and Applied Algebra, 2012, 219(3): 530-542.
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Ha H T, Sun M. Squarefree monomial ideals that fail the persistence property and non-increasing depth[C]., 2014, 40(1): 125-137.
3
Christopher A Francisco · Huy Tai Ha · Jeffrey Mermin. Powers of squarefree monomial ideals and combinatorics. 2013.
4
Louiza Fouli · Susan Morey. A lower bound for depths of powers of edge ideals. 2015.
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[8] Artinianness of local cohomology modules
Moharram Aghapournahr Department of Mathematics Faculty of Science, Arak University Leif Melkersson Department of Mathematics, Linköping University
Category Theory K-Theory and Homology mathscidoc:1701.04003
Arkiv for Matematik, 52, (1), 1-10, 2011.5
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[9] Equivariant Poincaré series of filtrations and topology
Antonio Campillo Instituto de Investigación en Matemáticas, Universidad de Valladolid Félix Delgado Instituto de Investigación en Matemáticas, Universidad de Valladolid Sabir M. Gusein-Zade Faculty of Mathematics and Mechanics, Moscow State University
K-Theory and Homology mathscidoc:1701.01021
Arkiv for Matematik, 52, (1), 43-59, 2012.5
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Earlier, for an action of a finite group$G$on a germ of an analytic variety, an equivariant$G$-Poincaré series of a multi-index filtration in the ring of germs of functions on the variety was defined as an element of the Grothendieck ring of$G$-sets with an additional structure. We discuss to which extent the$G$-Poincaré series of a filtration defined by a set of curve or divisorial valuations on the ring of germs of analytic functions in two variables determines the (equivariant) topology of the curve or of the set of divisors.
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[10] Maximal Marcinkiewicz multipliers
Petr Honzík Faculty of Mathematics and Physics, Charles University
Analysis of PDEs Functional Analysis mathscidoc:1701.03026
Arkiv for Matematik, 52, (1), 135-147, 2012.5
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Let $\mathcal{M} =\{m_{j}\}_{j=1}^{\infty}$ be a family of Marcinkiewicz multipliers of sufficient uniform smoothness in $\mathbb{R}^{n}$ . We show that the$L$^{$p$}norm, 1<$p$<∞, of the related maximal operator $$M_Nf(x)= \sup_{1\leq j \leq N} |\mathcal{F}^{-1} ( m_j \mathcal{F} f)|(x) $$ is at most$C$(log($N$+2))^{$n$/2}. We show that this bound is sharp.
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[11] Extrapolation from $A_{\infty}^{\rho,\infty}$ , vector-valued inequalities and applications in the Schrödinger settings
Lin Tang LMAM, School of Mathematical Science, Peking University
Analysis of PDEs mathscidoc:1701.03027
Arkiv for Matematik, 52, (1), 175-202, 2012.4
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In this paper, we generalize the$A$_{∞}extrapolation theorem ($Cruz-Uribe–Martell–Pérez$, Extrapolation from$A$_{∞}weights and applications,$J. Funct. Anal.$$213$(2004), 412–439) and the$A$_{$p$}extrapolation theorem of Rubio de Francia to Schrödinger settings. In addition, we also establish weighted vector-valued inequalities for Schrödinger-type maximal operators by using weights belonging to $A_{p}^{\rho,\infty }$ which includes$A$_{$p$}. As applications, we establish weighted vector-valued inequalities for some Schrödinger-type operators.
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Issue 2
[1] Global integral gradient bounds for quasilinear equations below or near the natural exponent
Nguyen Cong Phuc Department of Mathematics, Louisiana State University
Analysis of PDEs mathscidoc:1701.03028
Arkiv for Matematik, 52, (2), 329-354, 2012.6
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Nguyen Cong Phuc. Nonlinear Muckenhoupt-Wheeden type bounds on Reifenberg flat domains, with applications to quasilinear Riccati type equations. 2013.
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Baroni P, Castro A D, Palatucci G, et al. Global estimates for nonlinear parabolic equations[J]. Journal of Evolution Equations, 2013, 13(1): 163-195.
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Phuc N C. Morrey global bounds and quasilinear Riccati type equations below the natural exponent[J]. Journal de Mathématiques Pures et Appliquées, 2014, 102(1): 99-123.
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Adimurthi K, Phuc N C. Global Lorentz and Lorentz–Morrey estimates below the natural exponent for quasilinear equations[J]. Calculus of Variations and Partial Differential Equations, 2014, 54(3): 3107-3139.
5
Mengesha T, Phuc N C. Quasilinear Riccati type equations with distributional data in Morrey space framework[J]. Journal of Differential Equations, 2016, 260(6): 5421-5449.
6
Paolo Baroni · Agnese Di Castro · Giampiero Palatucci. FOR NONLINEAR PARABOLIC EQUATIONS. 2013.
Abstract
We obtain sharp integral potential bounds for gradients of solutions to a wide class of quasilinear elliptic equations with measure data. Our estimates are global over bounded domains that satisfy a mild exterior capacitary density condition. They are obtained in Lorentz spaces whose degrees of integrability lie below or near the natural exponent of the operator involved. As a consequence, nonlinear Calderón–Zygmund type estimates below the natural exponent are also obtained for $\mathcal{A}$ -superharmonic functions in the whole space ℝ^{$n$}. This answers a question raised in our earlier work (On Calderón–Zygmund theory for$p$- and $\mathcal{A}$ -superharmonic functions, to appear in$Calc. Var. Partial Differential Equations$, DOI10.1007/s00526-011-0478-8) and thus greatly improves the result there.
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[2] Nilpotent $p\mspace{1mu}$ -local finite groups
José Cantarero Centro de Investigación en Matemáticas, A.C., Guanajuato, Mexico Jérôme Scherer Mathematics Institute for Geometry and Applications, École Polytechnique Fédérale de Lausanne Antonio Viruel Departamento de Álgebra, Geometría y Topología, Universidad de Málaga
Group Theory and Lie Theory mathscidoc:1701.17004
Arkiv for Matematik, 52, (2), 203-225, 2012.5
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[3] On the weak-type (1,1) of the uncentered Hardy–Littlewood maximal operator associated with certain measures on the plane
Anna K. Savvopoulou Department of Mathematical Sciences, Indiana University South Bend Christopher M. Wedrychowicz Department of Mathematics and Computer Science, Saint Mary’s College
Classical Analysis and ODEs mathscidoc:1701.05005
Arkiv for Matematik, 52, (2), 367-382, 2012.11
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Suppose$μ$is a positive measure on $\mathbb{R}^{2}$ given by$μ$=$ν$×$λ$, where$ν$and$λ$are Radon measures on $\mathcal{S}^{1}$ and $\mathbb{R}^{{\mathchoice {\raise .17ex\hbox {$\scriptstyle +$}} {\raise .17ex\hbox {$\scriptstyle +$}} {\raise .1ex\hbox {$\scriptscriptstyle +$}} {\scriptscriptstyle +}}}$ , respectively, which do not vanish on any open interval. We prove that if for either$ν$or$λ$there exists a set of positive measure$A$in its domain for which the upper and lower$s$-densities, 0<$s$≤1, are positive and finite for every$x$∈$A$then the uncentered Hardy–Littlewood maximal operator$M$_{$μ$}is weak-type (1,1) if and only if$ν$is doubling and$λ$is doubling away from the origin. This generalizes results of Vargas concerning rotation-invariant measures on $\mathbb{R}^{n}$ when$n$=2.
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[4] Resonance-free region in scattering by a strictly convex obstacle
Long Jin Department of Mathematics, University of California, Berkeley
Analysis of PDEs Functional Analysis mathscidoc:1701.03029
Arkiv for Matematik, 52, (2), 257-289, 2012.12
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We prove the existence of a resonance-free region in scattering by a strictly convex obstacle $\mathcal{O}$ with the Robin boundary condition $\partial_{\nu}u+\gamma u|_{\partial\mathcal{O}}=0$ . More precisely, we show that the scattering resonances lie below a cubic curve ℑ$ζ$=−$S$|$ζ$|^{1/3}+$C$. The constant$S$is the same as in the case of the Neumann boundary condition$γ$=0. This generalizes earlier results on cubic pole-free regions obtained for the Dirichlet boundary condition.
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[5] $\mathcal{D}$ -modules with finite support are semi-simple
Rolf Källström Department of Mathematics, University of Gävle
Rings and Algebras mathscidoc:1701.31004
Arkiv for Matematik, 52, (2), 291-299, 2012.8
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Let $(R, \frak{m}, k_{R})$ be a regular local$k$-algebra satisfying the weak Jacobian criterion, and such that$k$_{$R$}/$k$is an algebraic field extension. Let $\mathcal{D}_{R}$ be the ring of$k$-linear differential operators of$R$. We give an explicit decomposition of the $\mathcal{D}_{R}$ -module $\mathcal{D}_{R}/\mathcal{D}_{R} \frak{m}_{R}^{n+1}$ as a direct sum of simple modules, all isomorphic to $\mathcal{D}_{R}/\mathcal{D}_{R} \frak{m}$ , where certain “Pochhammer” differential operators are used to describe generators of the simple components.
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[6] A modification of the Hodge star operator on manifolds with boundary
Ryszard L. Rubinsztein Department of Mathematics, Uppsala University
Geometric Analysis and Geometric Topology Rings and Algebras mathscidoc:1701.15005
Arkiv for Matematik, 52, (2), 355-365, 2012.12
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For smooth compact oriented Riemannian manifolds$M$of dimension 4$k$+2,$k$≥0, with or without boundary, and a vector bundle$F$on$M$with an inner product and a flat connection, we construct a modification of the Hodge star operator on the middle-dimensional (parabolic) cohomology of$M$twisted by$F$. This operator induces a canonical complex structure on the middle-dimensional cohomology space that is compatible with the natural symplectic form given by integrating the wedge product. In particular, when$k$=0 we get a canonical almost complex structure on the non-singular part of the moduli space of flat connections on a Riemann surface, with monodromies along boundary components belonging to fixed conjugacy classes when the surface has boundary, that is compatible with the standard symplectic form on the moduli space.
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[7] An improved Combes–Thomas estimate of magnetic Schrödinger operators
Zhongwei Shen Department of Mathematics and Statistics, Auburn University
Analysis of PDEs mathscidoc:1701.03030
Arkiv for Matematik, 52, (2), 383-414, 2013.1
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In the present paper, we prove an improved Combes–Thomas estimate, viz. the Combes–Thomas estimate in trace-class norms, for magnetic Schrödinger operators under general assumptions. In particular, we allow for unbounded potentials. We also show that for any function in the Schwartz space on the reals the operator kernel decays, in trace-class norms, faster than any polynomial.
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[8] CR singular images of generic submanifolds under holomorphic maps
Jiří Lebl Department of Mathematics, University of Wisconsin André Minor Department of Mathematics, University of California at San Diego Ravi Shroff Centre for Mathematics and its Applications Mathematical Sciences Institute, Australian National University Duong Son Department of Mathematics, University of California Yuan Zhang Department of Mathematical Sciences, Indiana University-Purdue University
Differential Geometry Geometric Analysis and Geometric Topology mathscidoc:1701.10015
Arkiv for Matematik, 52, (2), 301-327, 2012.11
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The purpose of this paper is to organize some results on the local geometry of CR singular real-analytic manifolds that are images of CR manifolds via a CR map that is a diffeomorphism onto its image. We find a necessary (sufficient in dimension 2) condition for the diffeomorphism to extend to a finite holomorphic map. The multiplicity of this map is a biholomorphic invariant that is precisely the Moser invariant of the image, when it is a Bishop surface with vanishing Bishop invariant. In higher dimensions, we study Levi-flat CR singular images and we prove that the set of CR singular points must be large, and in the case of codimension 2, necessarily Levi-flat or complex. We also show that there exist real-analytic CR functions on such images that satisfy the tangential CR conditions at the singular points, yet fail to extend to holomorphic functions in a neighborhood. We provide many examples to illustrate the phenomena that arise.
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[9] Reiteration theorems with extreme values of parameters
Pedro Fernández-Martínez Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia Teresa Signes Departamento de Matemática Aplicada, Facultad de Informática, Universidad de Murcia
Functional Analysis mathscidoc:1701.12025
Arkiv for Matematik, 52, (2), 227-256, 2012.12
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System Technologies. Limiting reiteration for real interpolation with logarithmic functions. 2016.
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Leo R Ya Doktorski. Limiting reiteration for real interpolation with logarithmic functions. 2016.
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Pedro Fernandezmartinez · Alba Segurado · Teresa Signes. Compactness Results for a Class of Limiting Interpolation Methods. 2016.
Abstract
We consider real interpolation methods defined by means of slowly varying functions$b$and symmetric spaces$E$, for which we present extreme reiteration theorems. As an application we identify, for all possible values of$θ$∈[0,1], the interpolation spaces ($L$_{1},$L$log$L$)_{$θ$,$b$,$E$}and ($L$_{exp},$L$_{∞})_{$θ$,$b$,$E$}.
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Impact Factor
0.744
Available
1949 - 2016
Volumes
60
Issues
119
Articles
1382