The bilinear Hilbert transform in UMD spaces
The bilinear Hilbert transform in UMD spaces
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UMD 空间中的双线性希尔伯特变换
DOI：
10.1007/s00208-020-02052-y
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发表时间：
2019
影响因子：
1.4
通讯作者：
G. Uraltsev
中科院分区：
文献类型：
--
作者：
Alex Amenta;G. Uraltsev
We prove Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-bounds for the bilinear Hilbert transform acting on functions valued in intermediate UMD spaces. Such bounds were previously unknown for UMD spaces that are not Banach lattices. Our proof relies on bounds on embeddings from Bochner spaces Lp(R;X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p(\mathbb {R};X)$$\end{document} into outer Lebesgue spaces on the time-frequency-scale space R+3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^3_+$$\end{document}.
We prove Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p$$\end{document}-bounds for the bilinear Hilbert transform acting on functions valued in intermediate UMD spaces. Such bounds were previously unknown for UMD spaces that are not Banach lattices. Our proof relies on bounds on embeddings from Bochner spaces Lp(R;X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^p(\mathbb {R};X)$$\end{document} into outer Lebesgue spaces on the time-frequency-scale space R+3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^3_+$$\end{document}.
外测度的 Lp 理论与 Lennart Carleson 的两个主题相结合
DOI：
10.1090/s0273-0979-2014-01474-0
发表时间：
2015
期刊：
arXiv: Classical Analysis and ODEs
影响因子：
--
作者：
C. Thiele
通讯作者：
C. Thiele
具有调制不变性的 Banach 值多线性奇异积分
影响因子：
1
作者：
Di Plinio, Francesco;Li, Kangwei;Martikainen, Henri;Vuorinen, Emil
通讯作者：
Vuorinen, Emil