Fractional Integration on Mixed Norm Spaces. II

被引:0
作者
Xiaolin Zhu
Xiang Fang
Feng Guo
Shengzhao Hou
机构
[1] Soochow University,School of Mathematics Science
[2] National Central University,Department of Mathematics
来源
The Journal of Geometric Analysis | 2023年 / 33卷
关键词
Fractional integration; Mixed norm space; Hardy space; BMOA; Bloch; Riemann–Liouville; 47B38; 26A33;
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摘要
In a previous paper Guo et al. (Fractional integration on mixed norm spaces. I. Preprint, 2022), we characterized the boundedness of fractional integration operators between mixed norm spaces over the unit disk. In this paper, we characterize the boundedness between X and Y, where X,Y∈{Hp(0<p<∞),H∞,BMOA,B,H(p,q,α)}.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} \begin{aligned} X, Y \in \{ H^p \ (0<p<\infty ),\ H^\infty ,\ \text {BMOA}, \ \mathcal {B}, \ H(p,q,\alpha ) \}. \end{aligned} \end{aligned}$$\end{document}As in Guo et al. (Fractional integration on mixed norm spaces. I. Preprint, 2022), we cover three types of fractional integration: Flett, Hadamard, and Riemann-Liouville, and we consider complex orders t∈C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t \in \mathbb {C}$$\end{document} instead of mere t∈R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t \in \mathbb {R}$$\end{document}. Our findings provide, in particular, a complete answer to a problem started by Flett in 1972 (Theorem C).
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