Hausdorff and Dunkl–Hausdorff operators in Lebesgue spaces for monotone functions and monotone weights

被引：0
作者：
Sandhya Jain
Pankaj Jain
机构：
[1] Vivekananda College (University of Delhi),Department of Mathematics
[2] South Asian University,Department of Mathematics
来源：
Positivity | 2023年 / 27卷
关键词：
Hausdorff operator; Dunkl–Hausdorff operator; Monotone functions; Boundedness; Sawyer’s duality principle; 47B38; 26D10; 26D15;
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摘要：
We characterize the Lvp(R+)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p_v(\mathbb {R}^+)$$\end{document}-Luq(R+)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^q_u(\mathbb {R}^+)$$\end{document} boundedness of the Hausdorff operator Hϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_\phi $$\end{document} on the cone of non-increasing functions for 1<p≤q<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1<p\le q<\infty $$\end{document} as well as 1<q<p<∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1<q<p<\infty $$\end{document}. We also consider the more general Dunkl–Hausdorff operator Hα,ϕ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\alpha ,\phi }$$\end{document} and characterize its weighted Lp(R+)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p(\mathbb {R}^+)$$\end{document} boundedness for monotone weights.
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