On boundedness of Hausdorff-type operators on Sobolev spaces

被引：0

作者：

Mirotin, A. R. ^{[1
,2
]}

机构：

[1] Francisk Skorina Gomel State Univ, Dept Math & Programming Technol, Gomel 246019, BELARUS

[2] Southern Fed Univ, Reg Math Ctr, Rostov Na Donu, Russia

来源：

INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS | 2025年 / 36卷 / 03期

关键词：

Hausdorff operator; Sobolev space; isometry; sharp conditions; HARDY-SPACES; HOMOGENEOUS SPACES; H-1;

D O I：

10.1080/10652469.2024.2411682

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new notion of a Hausdorff-type operator on function spaces over domains in Euclidean spaces is introduced, and a sufficient condition for the boundedness of this operator on Sobolev spaces is proved. It is shown that this condition cannot be weakened in general.

引用

页码：221 / 229

页数：9

共 23 条

[1]

Adams R., 2003, SOBOLEV SPACES

[2] Multivariate Hausdorff operators on the spaces Lp(Rn) [J].