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Weighted estimates for fractional maximal functions related to spherical means

Published online by Cambridge University Press:  17 April 2009

Michael Cowling ,
José García-Cuerva  and
Hendra Gunawan
Michael Cowling
Affiliation:
School of Mathematics, University of New South Wales, Sydney NSW 2052, Australia
José García-Cuerva
Affiliation:
Departamento de Matemáticas, C-XV, Universidad Autónoma de Madrid, 28049-Madrid, Spain
Hendra Gunawan
Affiliation:
Jurusan Matematika, Institut Teknologi Bandung, Bandung 40132, Indonesia
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Abstract

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We prove weighted Lp-Lq estimates for the maximal operators ℳα, given by , where μt denotes the normalised surface measure on the sphere of centre 0 and radius t in Rd. The techniques used involve interpolation and the Mellin transform. To do this, we also prove weighted Lp-Lq estimates for the operators of convolution with the kernels |·|−α−iη.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 66 , Issue 1 , August 2002 , pp. 75 - 90
Copyright
Copyright © Australian Mathematical Society 2002

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