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ESTIMATES FOR SINGULAR INTEGRALS ALONG SURFACES OF REVOLUTION

Part of: Harmonic analysis in several variables

Published online by Cambridge University Press:  01 June 2009

SHUICHI SATO
SHUICHI SATO*
Affiliation:
Department of Mathematics, Faculty of Education, Kanazawa University, Kanazawa 920-1192, Japan (email: shuichi@kenroku.kanazawa-u.ac.jp)
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Abstract

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We prove certain Lp estimates (1<p<∞) for nonisotropic singular integrals along surfaces of revolution. The singular integrals are defined by rough kernels. As an application we obtain Lp boundedness of the singular integrals under a sharp size condition on their kernels. We also prove a certain estimate for a trigonometric integral, which is useful in studying nonisotropic singular integrals.

Keywords

nonisotropic singular integralsextrapolationtrigonometric integrals

MSC classification

Secondary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 86 , Issue 3 , June 2009 , pp. 413 - 430
Copyright
Copyright © Australian Mathematical Society 2009

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