An intersection representation for a class of anisotropic vector-valued function spaces

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Abstract

The main result of this paper is an intersection representation for a class of anisotropic vector-valued function spaces in an axiomatic setting à la Hedberg and Netrusov (2007), which includes weighted anisotropic mixed-norm Besov and Lizorkin–Triebel spaces. In the special case of the classical Lizorkin–Triebel spaces, the intersection representation gives an improvement of the well-known Fubini property. The main result has applications in the weighted Lq-Lp-maximal regularity problem for parabolic boundary value problems, where weighted anisotropic mixed-norm Lizorkin–Triebel spaces occur as spaces of boundary data.

Original languageEnglish
Article number105519
Number of pages61
JournalJournal of Approximation Theory
Volume264
DOIs
Publication statusPublished - 2021

Keywords

  • Anisotropic
  • Axiomatic approach
  • Banach space-valued functions and distributions
  • Difference norm
  • Fubini property
  • Intersection representation
  • Maximal function
  • Quasi-Banach function space

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