Boundedness of averaging operators in weighted variable exponent spaces of periodic functions

IF 0.5 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2025-04-22 DOI:10.1007/s10476-025-00074-9

O. L. Vinogradov

引用次数: 0

Abstract

Sufficient conditions for the uniform boundedness of the Steklov averaging operators in weighted variable exponent spaces of periodic functions are obtained. The boundedness of the Steklov averages was previously known if the exponent satisfies the Dini-Lipschitz condition and a local analogue of the Muckenhoupt condition holds. In this paper, the boundedness of the Steklov averages is established under certain Muckenhoupt type conditions solely, and the Dini-Lipschitz condition is not required. The norms of averaging operators are estimated explicitly.

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周期函数加权变指数空间中平均算子的有界性

得到了周期函数加权变指数空间中Steklov平均算子一致有界的充分条件。如果指数满足Dini-Lipschitz条件和Muckenhoupt条件的局部模拟成立，那么Steklov平均的有界性是已知的。本文仅在某些Muckenhoupt型条件下建立了Steklov平均的有界性，而不需要Dini-Lipschitz条件。明确估计了平均算子的范数。

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.