Multiplier criteria of Marcinkiewicz type for Jacobi expansions-Reference-Cited by-同舟云学术

Multiplier criteria of Marcinkiewicz type for Jacobi expansions

Published:1977 Issue:1 Volume:231 Page:117-132
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Gasper George,Trebels Walter

Abstract

It is shown how an integral representation for the product of Jacobi polynomials can be used to derive a certain integral Lipschitz type condition for the Cesàro kernel for Jacobi expansions. This result is then used to give criteria of Marcinkiewicz type for a sequence to be multiplier of type (p, p), 1 > p > ∞ 1 > p > \infty , for Jacobi expansions.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1977-231-01/S0002-9947-1977-0467139-8/S0002-9947-1977-0467139-8.pdf

Reference18 articles.

1. W. N. Bailey, The generating function of Jacobi polynomials, J. London Math. Soc. 13 (1938), 8-12.

2. On 𝑀_{𝑝}^{𝑞} multipliers for Jacobi expansions;Bavinck, H.,1978

3. Sommes de Cesàro et multiplicateurs des développements en harmoniques sphériques;Bonami, Aline;Trans. Amer. Math. Soc.,1973

4. Note on the Bohr-Hardy theorem;Bosanquet, L. S.;J. London Math. Soc.,1942

5. Lecture Notes in Mathematics, Vol. 242;Coifman, Ronald R.,1971

Cited by 6 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Analysis Related to All Admissible Type Parameters in the Jacobi Setting;Constructive Approximation;2015-02-13

2. Hardy spaces for Dunkl–Gegenbauer expansions;Journal of Functional Analysis;2013-09

3. On the norms of generalized translation operators generated by the jacobi-dunkl operators;Journal of Mathematical Sciences;2012-04-10

4. Harmonic analysis associated with the Jacobi–Dunkl operator on ]-π2,π2[;Journal of Computational and Applied Mathematics;2005-06

5. Weighted estimates of singular integrals and their applications;Journal of Soviet Mathematics;1985-08