The bilinear Hilbert transform in UMD spaces

被引：8

作者：

Amenta, Alex ^{[1
]}

Uraltsev, Gennady ^{[2
]}

机构：

[1] Univ Bonn, Math Inst, Bonn, Germany

[2] Cornell Univ, Dept Math, White Hall, Ithaca, NY 14853 USA

来源：

MATHEMATISCHE ANNALEN | 2020年 / 378卷 / 3-4期

关键词：

VECTOR-VALUED INEQUALITIES; EXTRAPOLATION; CONVERGENCE; DOMINATION; OPERATORS; THEOREM;

D O I：

10.1007/s00208-020-02052-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove L-p-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 L-p(R; X) into outer Lebesgue spaces on the time-frequency-scale space R-+(3).

引用

页码：1129 / 1221

页数：93

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