Interpolation of compact bilinear operators among quasi-Banach spaces and applications

被引：14

作者：

Cobos, Fernando ^{[1
]}

Fernandez-Cabrera, Luz M. ^{[2
]}

Martinez, Anton ^{[3
]}

机构：

[1] Univ Complutense Madrid, Fac Matemat, Dept Anal Matemat & Matemat Aplicada, Plaza Ciencias 3, E-28040 Madrid, Spain

[2] Univ Complutense Madrid, Fac Estudios Estadist, Dept Anal Matemat & Matemat Aplicada, Secc Dept, E-28040 Madrid, Spain

[3] Univ Vigo, Escuela Ingn Ind, Dept Matemat Aplicada 1, Vigo 36200, Spain

来源：

MATHEMATISCHE NACHRICHTEN | 2018年 / 291卷 / 14-15期

关键词：

commutators of Calderon-Zygmund operators; compact bilinear operators; interpolation of compact bilinear operators among L-p-spaces; real interpolation of quasi-Banach couples; ARONSZAJN-GAGLIARDO FUNCTORS; REAL INTERPOLATION; LOGARITHMIC FUNCTORS; COMMUTATORS; REITERATION; PARAMETER; CALDERON; IDEALS;

D O I：

10.1002/mana.201700487

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the interpolation properties of compact bilinear operators by the general real method among quasi-Banach couples. As an application we show that commutators of Calderon-Zygmund bilinear operators S : L-p X L-q -> Lr are compact provided that 1/2 < r < 1, 1 < p,q < infinity and 1/p+1/q = 1/r.

引用

页码：2168 / 2187

页数：20

共 45 条

[1]

[Anonymous], 1992, Theory of function spaces, DOI DOI 10.1007/978-3-0346-0419-2

[2]

[Anonymous], 1986, Eigenvalue distribution of compact operators

[3]

[Anonymous], 1976, GRUNDLEHREN MATH WIS

[4]

[Anonymous], 1964, PUBL MATH I, DOI 10.1007/BF02684796

[5]

Bennett C., 1988, Interpolation of operators

[6] Smoothing of Commutators for a Hormander Class of Bilinear Pseudodifferential Operators [J].

Benyi, Arpad ;

Oh, Tadahiro .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2014, 20 (02) :282-300

[7]

Bényi A, 2013, P AM MATH SOC, V141, P3609

[8]

Brudnyi Y., 1991, INTERPOLATION FUNCTO, V1

[9]

Butzer P. L., 1967, GRUNDLEHREN MATH WIS, V145

[10]

Calderon A. P., 1951, STUD MATH, V12, DOI 10.4064/sm-12-1-194-204

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