A new scale of function spaces characterizing homogeneous Besov spaces

Fuente: arXiv
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Main Authors: Auscher, Pascal, Bechtel, Sebastian, Haardt, Luca
Format: Preprint
Published: 2025
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author Auscher, Pascal
Bechtel, Sebastian
Haardt, Luca
author_facet Auscher, Pascal
Bechtel, Sebastian
Haardt, Luca
contents We introduce and study a new scale of function spaces that characterize the homogeneous Besov spaces $\mathrm{\dot B}^β_{p,q}$, hence completing earlier work by Ullrich. These new spaces include the ones introduced by Barton and Mayboroda, and systematically studied by Amenta under the name of weighted $\mathrm{Z}$-spaces, for the purpose of boundary value problems with $\mathrm{\dot B}^β_{p,p}$ data. They are the counterparts to the weighted tent spaces with Whitney averages, developed by Huang, and arise as their real interpolants. We describe their functional analytic properties: completeness, duality, embeddings, as well as their real and complex interpolants.
format Preprint
id arxiv_https___arxiv_org_abs_2512_07399
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A new scale of function spaces characterizing homogeneous Besov spaces
Auscher, Pascal
Bechtel, Sebastian
Haardt, Luca
Classical Analysis and ODEs
Functional Analysis
42B35, 46E30, 46B70
We introduce and study a new scale of function spaces that characterize the homogeneous Besov spaces $\mathrm{\dot B}^β_{p,q}$, hence completing earlier work by Ullrich. These new spaces include the ones introduced by Barton and Mayboroda, and systematically studied by Amenta under the name of weighted $\mathrm{Z}$-spaces, for the purpose of boundary value problems with $\mathrm{\dot B}^β_{p,p}$ data. They are the counterparts to the weighted tent spaces with Whitney averages, developed by Huang, and arise as their real interpolants. We describe their functional analytic properties: completeness, duality, embeddings, as well as their real and complex interpolants.
title A new scale of function spaces characterizing homogeneous Besov spaces
topic Classical Analysis and ODEs
Functional Analysis
42B35, 46E30, 46B70
url https://arxiv.org/abs/2512.07399