Zhengwei LiuDepartment of Mathematics and Department of Physics, Harvard University, Cambridge, 02138, U.S.A. Simeng WangLaboratoire de Mathematiques, Universite de Franche -Comte, Besancon Cedex, 25030, France and Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckin 8, 00-956 Warszawa, PolandJinsong WuSchool of Mathematical Sciences, University of Science and Technology of China, Hefei, 230026, P.R. China
Spectral Theory and Operator Algebramathscidoc:2206.32001
Journal of Operator Theory, 77, (1), 109-131, 2017.12
In this paper, we generalize Young's inequality for locally compact quantum groups and obtain some results for extremal pairs of Young's inequality and extremal functions of Hausdorff-Young inequality.
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Let$χ$be an analytic vector field defined in a real-analytic manifold of dimension three. We prove that all the singularities of$χ$can be made elementary by a finite number of blowing-ups in the ambient space.