The Boundedness of Marcinkiewicz Integrals on Grand Variable Herz Spaces

被引：0
作者：
Xiao, Dan [1 ]
Shu, Lisheng [2 ]
机构：
[1] Anhui Profess Coll Art, Coll Humanities, Hefei 230001, Anhui, Peoples R China
[2] Anhui Normal Univ, Sch Math & Stat, Wuhu 241003, Anhui, Peoples R China
来源：
ANALYSIS IN THEORY AND APPLICATIONS | 2023年 / 39卷 / 02期
关键词：
Marcinkiewicz integrals; Herz spaces; variable exponent; grand spaces; L-P BOUNDS; FRACTIONAL INTEGRALS; GENERALIZED LEBESGUE; SOBOLEV SPACES; OPERATORS; COMMUTATORS;
D O I：
10.4208/ata.OA-2021-0007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Under some natural regularity assumptions on the exponent function, we obtain the boundedness of Marcinkiewicz integrals y, yPS and y*,P A on grand variable Herz spaces. Our results enrich and improve some previous results in the literature.
引用
收藏
页码：163 / 177
页数：15
相关论文
共 38 条
[1]  
Al-Salman A, 2002, MATH RES LETT, V9, P697
[2]  
Almeida A., 2006, J FUNCT SPACE APPL, V4, P113, DOI DOI 10.1155/2006/610535
[3]   Maximal, potential and singular type operators on Herz spaces with variable exponents [J].
Almeida, Alexandre ;
Drihem, Douadi .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2012, 394 (02) :781-795
[4]   CONVOLUTION OPERATORS ON BANACH SPACE VALUED FUNCTIONS [J].
BENEDEK, A ;
PANZONE, R ;
CALDERON, AP .
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1962, 48 (03) :356-&
[5]  
Capone C, 2007, REV MAT IBEROAM, V23, P743
[6]  
Castillo RE, 2016, CMS BOOKS MATH, P1, DOI 10.1007/978-3-319-30034-4
[7]   Riesz potential and Sobolev embeddings on generalized Lebesgue and Sobolev spaces Lp(•) and Wk,p [J].
Diening, L .
MATHEMATISCHE NACHRICHTEN, 2004, 268 :31-43
[8]  
Diening L, 2003, J REINE ANGEW MATH, V563, P197
[9]   Lebesgue and Sobolev Spaces with Variable Exponents [J].
Diening, Lars ;
Harjulehto, Petteri ;
Hasto, Peter ;
Ruzicka, Michael .
LEBESGUE AND SOBOLEV SPACES WITH VARIABLE EXPONENTS, 2011, 2017 :1-+
[10]  
Ding Y, 2000, ACTA MATH SIN, V16, P593, DOI 10.1007/PL00011567
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