A note on commutator estimates for interpolation methods

被引：1

作者：

Cerda, Joan ^{[1
]}

机构：

[1] Univ Barcelona, Dept Matemat Aplicada & Anal, E-08007 Barcelona, Spain

来源：

MATHEMATISCHE NACHRICHTEN | 2007年 / 280卷 / 9-10期

关键词：

interpolation method; interpolator; commutator; translation mapping; Benson norm; orbital method; lattice; pseudolattice;

D O I：

10.1002/mana.200510532

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this note is to show how all the commutator estimates of two recent papers, by M. Cwikel, N. Kalton, M. Milman, and R. Rochberg and by N. Krugljak and M. Milman, can be considered as special cases of the method of couples of interpolators introduced by M. J. Carro, J. Cerda and J. Soria, and also to show how the distance between orbits and the "Benson norm" considered by Krugljak and Milman can be extended, respectively, as a distance between the interpolators that appear in the general construction and as a constant that is finite when the interpolators satisfy the necessary cancellation property. (C) 2007 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim.

引用

页码：1014 / 1021

页数：8

共 21 条

[1]

Bergh J., 1976, INTERPOLATION SPACES

[2]

BRUDNYII YA, 1991, INTERPOLATION FUNCTO

[3] STABILITY IN INTERPOLATION OF FAMILIES OF BANACH-SPACES [J].

CAO, W ;

SAGHER, Y .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 112 (01) :91-100

[4] Higher order commutators in interpolation theory [J].

Carro, MJ ;

Cerda, J ;

Soria, J .

MATHEMATICA SCANDINAVICA, 1995, 77 (02) :301-319

[5] Commutators and interpolation methods [J].

Carro, MJ ;

Cerda, J ;

Soria, J .

ARKIV FOR MATEMATIK, 1995, 33 (02) :199-216

[6] SCHECHTER METHODS OF INTERPOLATION AND COMMUTATORS [J].

CARRO, MJ ;

CERDA, J ;

MILMAN, M ;

SORIA, J .

MATHEMATISCHE NACHRICHTEN, 1995, 174 :35-53

[7]

CARRO MJ, 1999, P INT WORKSH FUNCT S, V13, P24

[8] Commutators for approximation spaces and Marcinkiewicz-type multipliers [J].

Cerdà, J ;

Martín, J ;

Krugljak, NY .

JOURNAL OF APPROXIMATION THEORY, 1999, 100 (02) :251-265

[9] Commutators for Fourier multipliers on Besov spaces [J].

Cerdà, J ;

Martín, J .

JOURNAL OF APPROXIMATION THEORY, 2004, 129 (02) :119-128

[10] A unified theory of commutator estimates for a class of interpolation methods [J].

Cwikel, M ;

Kalton, N ;

Milman, M ;

Rochberg, R .

ADVANCES IN MATHEMATICS, 2002, 169 (02) :241-312

← 1 2 3 →