FRACTIONAL MAXIMAL OPERATOR AND FRACTIONAL INTEGRAL OPERATOR ON ORLICZ-LORENTZ SPACES

被引：0

作者：

Li, Hongliang ^{[1
]}

机构：

[1] Zhejiang Int Studies Univ, Dept Math, Hangzhou, Zhejiang, Peoples R China

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2016年 / 19卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Orlicz-Lorentz spaces; fractional maximal operator; fractional integral operator; modular inequalities; boundedness of operator; HARDY-TYPE; INEQUALITIES;

D O I：

10.7153/mia-19-02

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we prove the characterization of the weighted modular inequalities for the fractional maximal operator M-alpha (0 <= alpha< n) on the Orlicz-Lorentz spaces by atomic decomposition which induces a sufficient condition of the boundedness for this operator on the Orlicz-Lorentz spaces. And we also find the characterization of the weighted modular inequalities for the fractional integral operator I-alpha (0 <= alpha< n) on the Orlicz-Lorentz spaces in certain case which leads to a sufficient condition of the boundedness for I-alpha (0 <= alpha< n).

引用

页码：15 / 31

页数：17

共 30 条

[1] [Anonymous], 1961, Convex functions and Orlicz spaces
[2] Bennett C., 1980, Diss. Math, V175, P1
[3] Bennett C., 1988, PURE APPL MATH, V129
[4] WEIGHTED L-PHI INTEGRAL-INEQUALITIES FOR OPERATORS OF HARDY TYPE
BLOOM, S
KERMAN, R
[J]. STUDIA MATHEMATICA, 1994, 110 (01) : 35 - 52
[5] Carro MJ, 2007, MEM AM MATH SOC, V187, pIX
[6] WEIGHTED LORENTZ SPACES AND THE HARDY OPERATOR
CARRO, MJ
SORIA, J
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 1993, 112 (02) : 480 - 494
[7] Cianchi A, 1997, Q J MATH, V48, P439
[8] Heinig H. P., 2000, J INEQUAL PURE APPL, V1
[9] Abstract duality Sawyer formula and its applications
Kaminska, Anna
Mastylo, Mieczyslaw
[J]. MONATSHEFTE FUR MATHEMATIK, 2007, 151 (03): : 223 - 245
[10] INTEGRAL-INEQUALITIES WITH WEIGHTS FOR THE HARDY MAXIMAL-FUNCTION
KERMAN, RA
TORCHINSKY, A
[J]. STUDIA MATHEMATICA, 1982, 71 (03) : 277 - 284

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