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
收藏
页码：1137 / 1174
页数：38
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