MathSciDoc: An Archive for Mathematician ∫

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No abstract uploaded!

We characterize in geometric terms the zero sets of holomorphic functions$f$in the bidisk such that log |$f$|∈$L$^{$p$}($D$^{2}) for 1<$p$<∞.

It is known how to obtain a uniform estimate of e.g. a polynomial in terms of its logarithmic sum over the integers provided that the sum is sufficiently small. This result is generalized here and we obtain estimates in terms of logarithmic sums taken over certain discrete subsets of the real axis.

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First we define the dyadic Hardy space$H$_{$X$}$(d)$for an arbitrary rearrangement invariant space$X$on [0, 1]. We remark that previously only a definition of$H$_{$X$}$(d)$for$X$with the upper Boyd index$q$_{$x$}<∞ was available. Then we get a natural description of the dual space of$H$_{$x$}, in the case$X$having the property 1<-$p$_{$X$}<-$q$_{$X$}<2, imporoving an earlier result [P1].

In this paper, I study the group of analytic automorphisms of a bounded product domain in the space$C(S,C)$of continuous functions on a compact space$S$. I prove that its automorphism group is a Lie group and I am able to prove which are the bounded symmetric ones.

No abstract uploaded!

No abstract uploaded!

Let$X$and$Y$be closed subspaces of the Lorentz sequence space$d(v, p)$and the Orlicz sequence space$l$_{$M$}, respectively. It is proved that every bounded linear operator from$X$to$Y$is compact whenever $$p > \beta _M : = \inf \{ q > 0:\inf \{ M(\lambda t)/M(\lambda )t^q :0< \lambda ,t \leqslant 1\} > 0.$$ As an application, the reflexivity of the space of bounded linear operators acting from$d(v, p)$to$l$_{$M$}is characterized.