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

Lindemulder, Nick

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

Journal article (2021)

Authors

Nick Lindemulder Analysis - , Karlsruhe Institut für Technologie

Research Group

Analysis () (TU Delft)

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

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Published Date

2021

Language

English

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Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Delft Institute of Applied Mathematics

Research Group

Analysis

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 L_q-L_p-maximal regularity problem for parabolic boundary value problems, where weighted anisotropic mixed-norm Lizorkin–Triebel spaces occur as spaces of boundary data.

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