Multilinear Marcinkiewicz-Zygmund Inequalities

被引：5

作者：

Carando, Daniel ^{[1
,2
]}

Mazzitelli, Martin ^{[3
,4
]}

Ombrosi, Sheldy ^{[5
,6
]}

机构：

[1] Univ Buenos Aires, Dept Matemat Pab 1, Fac Cs Exactas & Nat, RA-1428 Buenos Aires, DF, Argentina

[2] Consejo Nacl Invest Cient & Tecn, IMAS, Buenos Aires, DF, Argentina

[3] Univ Nacl Cuyo, Inst Balseiro, CNEA, Buenos Aires, DF, Argentina

[4] Univ Nacl Comahue, Ctr Reg Univ Bariloche, Dept Matemat, RA-8400 San Carlos De Bariloche, Rio Negro, Argentina

[5] Univ Nacl Sur, Dept Matemat, RA-8000 Bahia Blanca, Buenos Aires, Argentina

[6] Consejo Nacl Invest Cient & Tecn, INMABB, Bahia Blanca, Buenos Aires, Argentina

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2019年 / 25卷 / 01期

关键词：

Vector-valued inequalities; Multilinear operators; Calderon-Zygmund operators; WEIGHTED NORM INEQUALITIES; VECTOR-VALUED INEQUALITIES; EXTRAPOLATION; SPACES;

D O I：

10.1007/s00041-017-9563-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We extend to the multilinear setting classical inequalities of Marcinkiewicz and Zygmund on r -valued extensions of linear operators. We show that for certain 1 = p, q1,..., qm, r = 8, there is a constant C = 0 such that for every bounded multilinear operator T : Lq1(mu 1) x center dot center dot center dot xLqm (mu m). L p(.) and functions {f 1 k1} n1 k1= 1. Lq1(mu 1),..., {f m km} nm km= 1. Lqm (mu m), the following inequality holds parallel to k1km | T ( f 1 k1,, f m km)| r.. 1/ r L p(.) = C T m i= 1 ni ki= 1 | f i ki | r.. 1/ r Lqi (mu i). (1) In some cases we also calculate the best constant C = 0 satisfying the previous inequality. We apply these results to obtain weighted vector-valued inequalities for multilinear Calderon-Zygmund operators.

引用

页码：51 / 85

页数：35

共 27 条

[1]

[Anonymous], 1985, Weighted Norm Inequalities and Related Topics

[2]

Benea C., ARXIV160901090

[3] MULTIPLE VECTOR-VALUED INEQUALITIES VIA THE HELICOIDAL METHOD [J].