THE HARDY-LITTLEWOOD THEOREM ON FRACTIONAL-INTEGRATION FOR LAGUERRE SERIES

被引：7

作者：

KANJIN, Y ^{[1
]}

SATO, E ^{[1
]}

机构：

[1] YAMAGATA UNIV,FAC SCI,DEPT MATH,YAMAGATA 990,JAPAN

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1995年 / 123卷 / 07期

关键词：

LAGUERRE POLYNOMIALS; FRACTIONAL INTEGRATION; MULTIPLIERS; TRANSPLANTATION;

D O I：

10.2307/2160953

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Hardy-Littlewood theorem on fractional integration for Fourier series says that if I(sigma)g similar to Sigma(n not equal 0) \n\(-sigma)($) over cap g(n)e(int), then I-sigma is bounded from L(p) to L(q), where 1 < p < q < infinity, 1/q = 1/p - sigma. We shall establish an analogue of this theorem for the Laguerre function system {(Gamma(n+alpha+1)/n!)(1/2) L(n)(alpha)(x)e(-x/2x alpha/2)}(infinity)(n=0).

引用

页码：2165 / 2171

页数：7

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