BEST CONSTANTS FOR 2 NONCONVOLUTION INEQUALITIES

被引：145

作者：

CHRIST, M ^{[1
]}

GRAFAKOS, L ^{[1
]}

机构：

[1] WASHINGTON UNIV,DEPT MATH,ST LOUIS,MO 63130

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1995年 / 123卷 / 06期

关键词：

D O I：

10.2307/2160978

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The norm of the operator which averages /f/ in L(p)(R(n)) over balls of radius delta/x/ centered at either 0 or x is obtained as a function of n, p and delta. Both inequalities proved are n-dimensional analogues of a classical inequality of Hardy in R(1). Finally, a lower bound for the operator norm of the Hardy-Littlewood maximal function on L(p)(R(n)) is given.

引用

页码：1687 / 1693

页数：7

共 8 条

[1] SPHERICAL REARRANGEMENTS, SUBHARMONIC FUNCTIONS, AND ]-FUNCTIONS IN N-SPACE [J].

BAERNSTEIN, A ;

TAYLOR, BA .

DUKE MATHEMATICAL JOURNAL, 1976, 43 (02) :245-268

[2] WEAK LEBESGUE SPACES AND QUANTUM-MECHANICAL BINDING [J].

FARIS, WG .

DUKE MATHEMATICAL JOURNAL, 1976, 43 (02) :365-373

[3]

Hardy G., 1959, INEQUALITIES

[4]

Polya G., 1951, ISOPERIMETRIC INEQUA

[5]

Sobolev S.L., 1938, MAT SBORNIK, V5, P471

[6]

Stein E. M., 1970, SINGULAR INTEGRAL DI

[7]

STEIN E. M., 1971, INTRO FOURIER ANAL E

[8] BEHAVIOR OF MAXIMAL FUNCTIONS IN RN FOR LARGE N [J].

STEIN, EM ;

STROMBERG, JO .

ARKIV FOR MATEMATIK, 1983, 21 (02) :259-269

← 1 →