Borderline Weighted Estimates for Commutators of Fractional Integrals

被引：1

作者：

Wang, Zhidan ^{[1
]}

Wu, Huoxiong ^{[2
]}

Xue, Qingying ^{[1
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Lab Math & Complex Syst, Minist Educ, Beijing 100875, Peoples R China

[2] Xiamen Univ, Sch Math Sci, Xiamen 361005, Fujian, Peoples R China

来源：

ANALYSIS IN THEORY AND APPLICATIONS | 2021年 / 37卷 / 03期

关键词：

Commutators; fractional integrals; borderline weighted estimates; Fefferman-Stein inequality; NORM INEQUALITIES; SINGULAR-INTEGRALS;

D O I：

10.4208/ata.2021.lu80.08

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let I-alpha,I-(b) over right arrow be the multilinear commutators of the fractional integrals I-alpha with the symbol (b) over right arrow = (b(1),..., b(k)). We show that the constant of borderline weighted estimates for I-alpha is 1/epsilon, and for I-alpha,I-(b) over right arrow is 1/epsilon(k+1) with each b(i) belongs to the Orlicz space Osc(exp) L(s)i.

引用

页码：404 / 425

页数：22

共 22 条

[1]

Carro MJ, 2005, INDIANA U MATH J, V54, P627

[2] Weighted estimates for a class of multilinear fractional type operators [J].

Chen, Xi ;

Xue, Qingying .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 362 (02) :355-373

[3] FACTORIZATION THEOREMS FOR HARDY SPACES IN SEVERAL VARIABLES [J].

COIFMAN, RR ;

ROCHBERG, R ;

WEISS, G .

ANNALS OF MATHEMATICS, 1976, 103 (03) :611-635

[4] Weighted endpoint estimates for commutators of fractional integrals [J].

Cruz-Uribe, D. ;

Fiorenza, Hartford A. .

CZECHOSLOVAK MATHEMATICAL JOURNAL, 2007, 57 (01) :153-160

[5] Endpoint estimates and weighted norm inequalities for commutators of fractional integrals [J].

Cruz-Uribe, D ;

Fiorenza, A .

PUBLICACIONS MATEMATIQUES, 2003, 47 (01) :103-131

[6]

Cruz-Uribe DV, 2011, OPER THEORY ADV APPL, V215, P3, DOI 10.1007/978-3-0348-0072-3

[7] Weak estimates for commutators of fractional integral operators [J].

Ding, Y ;

Lu, SZ ;

Zhang, P .

SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY, 2001, 44 (07) :877-888

[8] Borderline weak-type estimates for singular integrals and square functions [J].

Domingo-Salazar, Carlos ;

Lacey, Michael ;

Rey, Guillermo .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2016, 48 :63-73

[9] SOME MAXIMAL INEQUALITIES [J].

FEFFERMAN, C ;

STEIN, EM .

AMERICAN JOURNAL OF MATHEMATICS, 1971, 93 (01) :107-+

[10] The L(log L)ε endpoint estimate for maximal singular integral operators [J].

Hytonen, Tuomas ;

Perez, Carlos .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 428 (01) :605-626

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