Heat-diffusion maximal operators for Laguerre semigroups with negative parameters

被引：25

作者：

Macías, R ^{[1
]}

Segovia, C

Torrea, JL

机构：

[1] Univ Autonoma Madrid, Dept Matemat, Fac Ciencias, E-28049 Madrid, Spain

[2] Univ Nacl Litoral, IMAL, FIQ, CONICET, RA-3000 Santa Fe, Argentina

[3] Consejo Nacl Invest Cient & Tecn, Inst Argentino Matemat, Buenos Aires, DF, Argentina

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2005年 / 229卷 / 02期

关键词：

heat and Poisson semigroups; Laguerre functions;

D O I：

10.1016/j.jfa.2005.02.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove L-P boundedness for the maximal operator of the heat semigroup associated to the Laguerre functions, {L-k(x)}(k), when the parameter a is greater than -1. Namely, the maximal operator is of strong type (p, p) if p > 1 and 2/2+alpha < p < 2/-alpha, when -1 < alpha < 0. If alpha > 0 there is strong type for 1 < p < infinity. The behavior at the end points is studied in detail. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：300 / 316

页数：17

共 9 条

[1]

DEGUZMAN M, 1981, N HOLLAND MATH STUDI, V46

[2]

Erdelyi A., 1953, HIGHER TRANSCENDENTA, VII

[3] POISSON INTEGRALS FOR HERMITE AND LAGUERRE EXPANSIONS [J].

MUCKENHOUPT, B .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 139 (MAY) :231-+

[4] WEIGHTED NORM INEQUALITIES FOR HARDY MAXIMAL FUNCTION [J].

MUCKENHOUPT, B .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 165 (MAR) :207-+

[5]

Stein E. S., 1970, PRINCETON MATH SERIE, V30

[6]

Stein EM, 1970, ANN MATH STUDIES, V63

[7]

STEMPAK K, 1994, TOHOKU MATH J, V46, P83, DOI 10.2748/tmj/1178225803

[8]

Szego G., 1939, AM MATH SOC C PUBLIC, V23

[9]

THANGAVELU S, 1993, MATH NOTES, V24

← 1 →