Rearrangement Estimates and Limiting Embeddings for Anisotropic Besov Spaces

IF 0.6 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2023-10-09 DOI:10.1007/s10476-023-0241-3

V. I. Kolyada

引用次数: 0

Abstract

The paper is dedicated to the study of embeddings of the anisotropic Besov spaces \(B_{p,{\theta _1}, \ldots ,{\theta _n}}^{{\beta _1}, \ldots ,{\beta _n}}\) (ℝⁿ) into Lorentz spaces. We find the sharp asymptotic behaviour of embedding constants when some of the exponents β_k tend to 1 (β_k < 1). In particular, these results give an extension of the estimate proved by 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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各向异性Besov空间的重排估计和限制嵌入

本文主要研究各向异性贝索夫空间\(B_{p,{\theta _1}, \ldots ,{\theta _n}}^{{\beta _1}, \ldots ,{\beta _n}}\) (n)在洛伦兹空间中的嵌入问题。当某些指数βk趋于1时，我们发现嵌入常数具有明显的渐近性(βk ＆lt;特别地，这些结果给出了Bourgain, Brezis和Mironescu对各向同性Besov空间的估计的推广。此外，在极限情况下，我们还得到了具有已知各向异性Lipschitz空间嵌入的链路。本文的主要成果之一是利用连续性的偏模估计重排的各向异性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis Mathematica MATHEMATICS-

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Traditionally the emphasis of Analysis Mathematica is classical analysis, including real functions (MSC 2010: 26xx), measure and integration (28xx), functions of a complex variable (30xx), special functions (33xx), sequences, series, summability (40xx), approximations and expansions (41xx). The scope also includes potential theory (31xx), several complex variables and analytic spaces (32xx), harmonic analysis on Euclidean spaces (42xx), abstract harmonic analysis (43xx). The journal willingly considers papers in difference and functional equations (39xx), functional analysis (46xx), operator theory (47xx), analysis on topological groups and metric spaces, matrix analysis, discrete versions of topics in analysis, convex and geometric analysis and the interplay between geometry and analysis.