On the Multilinear Fractional Integral Operators with Correlation Kernels

被引：4

作者：

Shi, Zuoshunhua ^{[1
,2
]}

Wu, Di ^{[3
]}

Yan, Dunyan ^{[3
]}

机构：

[1] Cent S Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

[2] Chinese Acad Sci, Grad Univ, Sch Math Sci, Beijing 100049, Peoples R China

[3] Chinese Acad Sci, Grad Univ, Sch Math Sci, Beijing 100190, Peoples R China

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2019年 / 25卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Multilinear fractional integral operator; Correlation kernels; Brascamp-Lieb inequality; Selberg integral; INEQUALITIES; CONSTANTS;

D O I：

10.1007/s00041-017-9591-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study a class of multilinear fractional integral operators associated with correlation kernels 1i<jk|xi-xj|-ij. We obtain the necessary and sufficient condition under which these operators are bounded from Lp1xxLpk into Lq. As a consequence, we also get the endpoint estimates from Lp1xxLpk to BMO.

引用

页码：538 / 587

页数：50

共 26 条

[1]

[Anonymous], THESIS

[2] On a reverse form of the Brascamp-Lieb inequality [J].

Barthe, F .

INVENTIONES MATHEMATICAE, 1998, 134 (02) :335-361

[3]

Beckner W, 2013, ARXIV13116747

[4]

Beckner W., 1995, ESSAYS FOURIER ANAL, V42, P36

[5] Functionals for Multilinear Fractional Embedding [J].

Beckner, William .

ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2015, 31 (01) :1-28

[6] The Brascamp-Lieb inequalities: Finiteness, structure and extremals [J].

Bennett, Jonathan ;

Carbery, Anthony ;

Christ, Michael ;

Tao, Terence .

GEOMETRIC AND FUNCTIONAL ANALYSIS, 2007, 17 (05) :1343-1415

[7]

Bennett J, 2010, MATH RES LETT, V17, P647

[8] BEST CONSTANTS IN YOUNGS INEQUALITY, ITS CONVERSE, AND ITS GENERALIZATION TO MORE THAN 3 FUNCTIONS [J].

BRASCAMP, HJ ;

LIEB, EH .

ADVANCES IN MATHEMATICS, 1976, 20 (02) :151-173

[9] ON THE RESTRICTION OF THE FOURIER-TRANSFORM TO CURVES - ENDPOINT RESULTS AND THE DEGENERATE CASE [J].

CHRIST, M .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1985, 287 (01) :223-238

[10]

Fan K, 1956, Ann. Math. Stud., V38, P99

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