OPTIMAL REARRANGEMENT-INVARIANT BANACH FUNCTION RANGE FOR THE HILBERT TRANSFORM

被引：2

作者：

Tulenov, K. S. ^{[1
,2
]}

机构：

[1] Al Farabi Kazakh Natl Univ, Dept Mech & Math, 71 Al Farabi Ave, Alma Ata 050040, Kazakhstan

[2] Inst Math & Math Modeling, 71 Al Farabi Ave, Alma Ata 050040, Kazakhstan

来源：

EURASIAN MATHEMATICAL JOURNAL | 2021年 / 12卷 / 02期

关键词：

rearrangement-invariant Banach function space; Hilbert transform; optimal range; SOBOLEV IMBEDDINGS; OPTIMAL DOMAIN;

D O I：

10.32523/2077-9879-2021-12-2-90-103

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe the optimal rearrangement-invariant Banach function range of the classical Hilbert transform acting on a rearrangement-invariant Banach function space. We also show the existence of such optimal range for the Lorentz and Marcinkiewicz spaces.

引用

页码：90 / 103

页数：14

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