Journal of Operator Theory

Volume 67, Issue 2, Spring 2012 pp. 349-368.

Hardy-Littlewood and UMD Banach lattices via Bessel convolution operators

Authors: Jorge J. Betancor (1), Juan C. Farina (2), and Lourdes Rodriguez-Mesa (3)
Author institution: (1) Departamento de Analisis Matematico, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofisico Fco. Sanchez, s/n, 38271 La Laguna (Sta. Cruz de Tenerife), Spain
(2) Departamento de Analisis Matematico, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofisico Fco. Sanchez, s/n, 38271 La Laguna (Sta. Cruz de Tenerife), Spain
(3) Departamento de Analisis Matematico, Universidad de la Laguna, Campus de Anchieta, Avda. Astrofisico Fco. Sanchez, s/n, 38271 La Laguna (Sta. Cruz de Tenerife), Spain

Summary: In this paper we characterize the Banach lattices having the UMD and the Hardy-Littlewood properties by using Littlewood--Paley $g$-functions for the Poisson semigroup and maximal operators associated with convolution operators in the Bessel setting.

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