Boundedness of the Hilbert Transform in Besov Spaces

被引：1

作者：

Ushakova, E. P. ^{[1
,2
,3
]}

机构：

[1] Russian Acad Sci, VA Trapeznikov Inst Control Sci, 65 Profsoyuznaya Str, Moscow 117997, Russia

[2] Russian Acad Sci, Steklov Math Inst, 8 Gubkina Str, Moscow 119991, Russia

[3] Russian Acad Sci, Comp Ctr, Far Eastern Branch, 65 Kim Yu Chena Str, Khabarovsk 680000, Russia

来源：

ANALYSIS MATHEMATICA | 2023年 / 49卷 / 04期

基金：

俄罗斯科学基金会;

关键词：

Hilbert transform; Riemann-Liouville operator of fractional integration; weighted Besov space; weighted Triebel-Lizorkin space; Muckenhoupt weight; REAL VARIABLE CHARACTERIZATION; WEIGHTED NORM INEQUALITIES; BLOCK SPIN CONSTRUCTION; 2-WEIGHT INEQUALITY; MUCKENHOUPT WEIGHTS; ONDELETTES;

D O I：

10.1007/s10476-023-0242-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 , 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.

引用

页码：1137 / 1174

页数：38

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