Rearrangement estimates and limiting embeddings for anisotropic Besov spaces

2023/06/24 by V. I. Kolyada, Kolyada, V. I.
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2306.13938

openalex publication_date 2023/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The paper is dedicated to the study of embeddings of the anisotropic Besov spaces Bβ1,...,betanp;θ1,...,θn(\Bbb Rn) into Lorentz spaces. We find the sharp asymptotic behaviour of embedding constants when some of the exponents βk tend to 1 (βk<1). In particular, these results give an extension of the estimate proved btý Bourgain, Brezis, and Mironescu for isotropic Besov spaces. Also, in the limit, we obtain a link with some known embeddings of anisotropic Lipschitz spaces. One of the key results of the paper is an anisotropic type estimate of rearrangements in terms of partial moduli of continuity.

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