REMARK ON SINGULAR INTEGRAL OPERATORS OF CONVOLUTION TYPE ON REARRANGEMENT-INVARIANT BANACH FUNCTION SPACES

被引：0

作者：

Karlovych, Oleksiy ^{[1
]}

Shargorodsky, Eugene ^{[2
,3
]}

机构：

[1] Univ Nova Lisboa, Fac Ciencias & Tecnol, Dept Matemat, Ctr Matemat & Aplicacoes, P-2829516 Caparica, Portugal

[2] Kings Coll London, Dept Math, London WC2R 2LS, England

[3] Tech Univ Dresden, Fak Math, D-01062 Dresden, Germany

来源：

REAL ANALYSIS EXCHANGE | 2023年 / 48卷 / 01期

关键词：

Calder ' on-Zygmund singular integral operators of convolution type; rearrangement-invariant Banach function spaces; Boyd indices;

D O I：

10.14321/realanalexch.48.1.1661058123

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that nondegenerate singular integral operators of convolution type are bounded on a rearrangement-invariant Banach function space X(R-d) if and only if its Boyd indices are nontrivial, extending the result by David Boyd (1966) for the Hilbert transform.

引用

页码：139 / 148

页数：10

共 12 条

[1]

Bennett C., 1988, Pure and Applied Mathematics, VVol. 129

[2]

Boyd D. W., 1966, Thesis (Ph.D.)

[3] INDICES OF FUNCTION SPACES AND THEIR RELATIONSHIP TO INTERPOLATION [J].