New results on restriction of Fourier multipliers

被引：3

作者：

Carro, Maria ^{[1
]}

Rodriguez, Salvador ^{[1
]}

机构：

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

来源：

MATHEMATISCHE ZEITSCHRIFT | 2010年 / 265卷 / 02期

关键词：

SEPARATION-PRESERVING REPRESENTATIONS; MAXIMAL OPERATORS; LORENTZ SPACES; CONVOLUTION OPERATORS; SINGULAR-INTEGRALS; TRANSFERENCE; INEQUALITIES; CURVES;

D O I：

10.1007/s00209-009-0522-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We develop an extension of the Transference methods introduced by R. Coifman and G. Weiss and apply it to study the problem of the restriction of Fourier multipliers between rearrangement invariant spaces, obtaining natural extensions of the classical de Leeuw's result and its further extension to maximal Fourier multipliers due to C. Kenig and P. Tomas.

引用

页码：417 / 435

页数：19

共 26 条

[1]

[Anonymous], C MATH SOC JANOS BOL

[2]

ASMAR N, 1990, CR ACAD SCI I-MATH, V311, P173

[3]

ASMAR N, 1989, CR ACAD SCI I-MATH, V309, P163

[4] TRANSFERENCE OF STRONG TYPE MAXIMAL INEQUALITIES BY SEPARATION-PRESERVING REPRESENTATIONS [J].

ASMAR, N ;

BERKSON, E ;

GILLESPIE, TA .

AMERICAN JOURNAL OF MATHEMATICS, 1991, 113 (01) :47-74

[5]

Bennett C., 1988, PURE APPL MATH, V129

[6] Diseretization and transferenee of bisublinear maximal operators [J].

Berkson, Earl ;

Blasco, Oscar ;

Carro, Maria J. ;

Gillespie, T. A. .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2006, 12 (04) :447-481

[7] Singular integrals in the Cesaro sense [J].

Bernardis, AL ;

Martín-Reyes, FJ .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2000, 6 (02) :143-152

[8] Bilinear Hilbert transform on measure spaces [J].

Blasco, O ;

Carro, M ;

Gillespie, TA .

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 2005, 11 (04) :459-470

[9] Transference of bilinear multiplier operators on Lorentz spaces [J].

Blasco, O ;

Villarroya, F .

ILLINOIS JOURNAL OF MATHEMATICS, 2003, 47 (04) :1327-1343

[10]

Carro MJ, 2007, MEM AM MATH SOC, V187, pIX

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