MULTIPARAMETER SINGULAR-INTEGRALS AND MAXIMAL FUNCTIONS

被引：91

作者：

RICCI, F

STEIN, EM

机构：

[1] POLITECN TORINO, DIPARTIMENTO MATEMAT, I-10129 TURIN, ITALY

[2] PRINCETON UNIV, DEPT MATH, PRINCETON, NJ 08544 USA

来源：

ANNALES DE L INSTITUT FOURIER | 1992年 / 42卷 / 03期

关键词：

SINGULAR INTEGRALS; MAXIMAL FUNCTIONS; CALDERON-ZYGMUND KERNELS; PRODUCT DOMAINS;

D O I：

10.5802/aif.1304

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove L(p)-boundedness for a class of singular integral operators and maximal operators associated with a general k-parameter family of dilations on R(n). This class includes homogeneous operators defined by kernels supported on homogeneous manifolds. For singular integrals, only certain << minimal >> cancellation is required of the kernels, depending on the given set of dilations.

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收藏

页码：637 / 670

页数：34

相关论文

共 21 条

[1] DIFFERENTIATION IN LACUNARY DIRECTIONS AND AN EXTENSION OF THE MARCINKIEWICZ MULTIPLIER THEOREM [J].

CARBERY, A .

ANNALES DE L INSTITUT FOURIER, 1988, 38 (01) :157-168

[2]

CARBERY A, HP LP VARIANTS MULTI

[3] ESTIMATES FOR MAXIMAL FUNCTIONS ALONG HYPERSURFACES [J].

CARLSSON, H ;

SJOGREN, P .

ARKIV FOR MATEMATIK, 1987, 25 (01) :1-14

[4] MULTIPARAMETER MAXIMAL FUNCTIONS ALONG DILATION-INVARIANT HYPERSURFACES [J].

CARLSSON, H ;

SJOGREN, P ;

STROMBERG, JO .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1985, 292 (01) :335-343

[5] HILBERT-TRANSFORMS ALONG CURVES .1. NILPOTENT GROUPS [J].

CHRIST, M .

ANNALS OF MATHEMATICS, 1985, 122 (03) :575-596

[6]

CHRIST M, IN PRESS T AM MATH S

[7] EQUIVALENCE BETWEEN BOUNDEDNESS OF CERTAIN CLASSES OF MAXIMAL AND MULTIPLIER OPERATORS IN FOURIER-ANALYSIS [J].

CORDOBA, A ;

FEFFERMAN, R .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1977, 74 (02) :423-425

[8] MAXIMAL AND SINGULAR INTEGRAL-OPERATORS VIA FOURIER-TRANSFORM ESTIMATES [J].

DUOANDIKOETXEA, J ;

DEFRANCIA, JLR .

INVENTIONES MATHEMATICAE, 1986, 84 (03) :541-561

[9] MULTIPLE SINGULAR-INTEGRALS AND MAXIMAL FUNCTIONS ALONG HYPERSURFACES [J].

DUOANDIKOETXEA, J .

ANNALES DE L INSTITUT FOURIER, 1986, 36 (04) :185-206

[10] CALDERON-ZYGMUND THEORY FOR PRODUCT DOMAINS - HP SPACES [J].

FEFFERMAN, R .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1986, 83 (04) :840-843