2 NOTES ON CONVERGENCE AND DIVERGENCE AE OF FOURIER-SERIES WITH RESPECT TO SOME ORTHOGONAL SYSTEMS

被引：16

作者：

GUADALUPE, JJ ^{[1
]}

PEREZ, M ^{[1
]}

RUIZ, FJ ^{[1
]}

VARONA, JL ^{[1
]}

机构：

[1] COLEGIO UNIV LA RIOJA, DEPT MATEMAT APLI, E-26001 LOGRONO, SPAIN

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1992年 / 116卷 / 02期

关键词：

FOURIER SERIES; ORTHONORMAL POLYNOMIALS; MAXIMAL OPERATORS; A(P)-WEIGHTS;

D O I：

10.2307/2159752

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study some problems related to convergence and divergence a.e. for Fourier series in systems {phi(k)} , where {phi(k)} is either a system of orthonormal polynomials with respect to a measure d mu on [-1 , 1] or a Bessel system on [0, 1]. We obtain boundedness in weighted L(p) spaces for the maximal operators associated to Fourier-Jacobi and Fourier-Bessel series. On the other hand, we find general results about divergence a.e. of the Fourier series associated to Bessel systems and systems of orthonormal polynomials on [-1 , 1] .

引用

页码：457 / 464

页数：8

共 16 条

[1] A TRANSPLANTATION THEOREM FOR JACOBI SERIES [J].

ASKEY, R .

ILLINOIS JOURNAL OF MATHEMATICS, 1969, 13 (03) :583-&

[2]

Benedek A., 1972, REV UN MAT ARGENTINA, V26, P167

[3] ON CONVERGENCE AND GROWTH OF PARTIAL SUMS OF FOURIER SERIES [J].

CARLESON, L .

ACTA MATHEMATICA UPPSALA, 1966, 116 (1-2) :135-&

[4] MAXIMAL THEOREMS FOR SOME ORTHOGONAL SERIES .1. [J].

GILBERT, JE .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 145 :495-&

[5] WEIGHTED NORM INEQUALITIES FOR CONJUGATE FUNCTION AND HILBERT TRANSFORM [J].

HUNT, R ;

MUCKENHOUPT, B ;

WHEEDEN, R .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 176 (449) :227-251

[6]

Hunt R.A., 1968, P C ORTHOGONAL EXPAN, P235

[7] WEIGHTED NORM INEQUALITY FOR FOURIER-SERIES [J].

HUNT, RA ;

YOUNG, WS .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 80 (02) :274-277

[8] NECESSARY CONDITIONS FOR WEIGHTED MEAN CONVERGENCE OF FOURIER-SERIES IN ORTHOGONAL POLYNOMIALS [J].

MATE, A ;

NEVAI, P ;

TOTIK, V .

JOURNAL OF APPROXIMATION THEORY, 1986, 46 (03) :314-322

[9] DIVERGENT JACOBI POLYNOMIAL SERIES [J].

MEANEY, C .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1983, 87 (03) :459-462

[10]

MUCHENHOUPT B, 1986, MEM AM MATH SOC 356, V64

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