Boundedness of the Hilbert Transform in Besov Spaces

被引：0
|
作者：
E. P. Ushakova
机构：
[1] V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences,
[2] Steklov Mathematical Institute of Russian Academy of Sciences,undefined
[3] Computing Center of Far Eastern Branch of Russian Academy of Sciences,undefined
来源：
Analysis Mathematica | 2023年 / 49卷
关键词：
Hilbert transform; Riemann–Liouville operator of fractional integration; weighted Besov space; weighted Triebel–Lizorkin space; Muckenhoupt weight; 44A15; 26A33;
D O I：
暂无
中图分类号：
学科分类号：
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 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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页码：1137 / 1174
页数：37
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