Boundedness criterion for integral operators on the fractional Fock–Sobolev spaces
Boundedness criterion for integral operators on the fractional Fock–Sobolev spaces
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DOI：
10.1007/s00209-022-03050-3
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发表时间：
2021-01
影响因子：
0.8
通讯作者：
G. Cao;Li He;Ji Li;Minxing Shen
中科院分区：
文献类型：
--
作者：
G. Cao;Li He;Ji Li;Minxing Shen
We provide a boundedness criterion for the integral operatoron the fractional Fock–Sobolev space,, where(introduced by Zhu ) is given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} S_{\varphi }F(z):= \int _{{\mathbb {C}}^n} F(w) e^{z \cdot \bar{w}} \varphi (z- \bar{w}) d\lambda (w) \end{aligned}$$\end{document}within the Fock spaceandthe Gaussian measure on the complex space. This extends the recent result in Cao et al. (Adv Math 363: 107001, 33 pp, 2020). The main approach is to develop multipliers on the fractional Hermite–Sobolev space.
We provide a boundedness criterion for the integral operatoron the fractional Fock–Sobolev space,, where(introduced by Zhu ) is given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{aligned} S_{\varphi }F(z):= \int _{{\mathbb {C}}^n} F(w) e^{z \cdot \bar{w}} \varphi (z- \bar{w}) d\lambda (w) \end{aligned}$$\end{document}within the Fock spaceandthe Gaussian measure on the complex space. This extends the recent result in Cao et al. (Adv Math 363: 107001, 33 pp, 2020). The main approach is to develop multipliers on the fractional Hermite–Sobolev space.