Besov空间中Hilbert变换的有界性

IF 0.6 3区数学 Q3 MATHEMATICS

Analysis Mathematica Pub Date : 2023-11-15 DOI:10.1007/s10476-023-0242-2

E. P. Ushakova

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引用次数: 0

摘要

得到了权值为Muckenhoupt的Besov空间中Hilbert变换H的有界性条件。在这种情况下，算子H作用于Hardy空间中函数的子类。本文利用Riemann-Liouville分数阶积分算子表示Hilbert变换H，并在图像和预像的范数上建立了独立估计。另外，给出了约束于Schwartz函数子类的加权Besov和triiebel - lizorkin空间中的变换H的有界性判据。

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Boundedness of the Hilbert Transform in Besov Spaces

Boundedness conditions are found for the Hilbert transform H in Besov spaces with Muckenhoupt weights. The operator H in this situation acts on subclasses of functions from Hardy spaces. The results are obtained by representing the Hilbert transform H via Riemann–Liouville operators of fractional integration on ℝ, on the norms of images and pre-images of which independent estimates are established in the paper. Separately, a boundedness criterion is given for the transform H in weighted Besov and Triebel–Lizorkin spaces restricted to the subclass of Schwartz functions.

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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.