On a Littlewood-Paley type inequality

被引：4

作者：

Djordjevic, Olivera

Pavlovic, Miroslav

机构：

[1] Fak Org Nauka, Belgrade, Serbia

[2] Matemat Fak, Belgrade, Serbia

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2007年 / 135卷 / 11期

关键词：

Littlewood-Paley inequalities; harmonic functions in R-N;

D O I：

10.1090/S0002-9939-07-09016-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The following is proved: If u is a function harmonic in the unit ball B subset of R-N and if 0 < p <= 1, then the inequality integral(partial derivative B) u*( y)(p) d sigma <= C-p,C-N (vertical bar u( 0)|(p) + integral(B) ( 1 -vertical bar x vertical bar)(p-1) vertical bar del u( x)vertical bar p dV (x)) holds, where u* is the nontangential maximal function of u. This improves a recent result of Stoll. This inequality holds for polyharmonic and hyperbolically harmonic functions as well.

引用

页码：3607 / 3611

页数：5

共 18 条

[1]

[Anonymous], 1994, PUBLICATIONS LINSTIT

[2]

[Anonymous], 1936, P LOND MATH SOC, DOI 10.1112/plms/s2-42.1.52

[3]

FEFFERMAN C, 1972, ACTA MATH-UPPSALA, V129, P137, DOI 10.1007/BF02392215

[4] MEAN VALUES OF POWER SERIES [J].

FLETT, TM .

PACIFIC JOURNAL OF MATHEMATICS, 1968, 25 (03) :463-&

[5]

GARNETT JB, 1981, BOUNDED ALAL FUNCTIO, V96

[6]

Hardy GH, 1932, J REINE ANGEW MATH, V167, P405

[7]

JECTIC M, 1993, ARCH MATH, V61, P367

[8]

Jevtic M, 1999, INDIAN J PURE AP MAT, V30, P407

[9] A NEW PROOF OF AN INEQUALITY OF LITTLEWOOD AND PALEY [J].

LUECKING, DH .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 103 (03) :887-893

[10] INEQUALITIES FOR THE GRADIENT OF EIGENFUNCTIONS OF THE INVARIANT LAPLACIAN IN THE UNIT BALL [J].

PAVLOVIC, M .

INDAGATIONES MATHEMATICAE-NEW SERIES, 1991, 2 (01) :89-98

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