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A NOTE ON MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION

Part of: Integral, integro-differential, and pseudodifferential operators Harmonic analysis in several variables

Published online by Cambridge University Press:  14 August 2017

FENG LIU
FENG LIU*
Affiliation:
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, China email [email protected]
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Abstract

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We establish the bounds of Marcinkiewicz integrals associated to surfaces of revolution generated by two polynomial mappings on Triebel–Lizorkin spaces and Besov spaces when their integral kernels are given by functions $\unicode[STIX]{x1D6FA}\in H^{1}(\text{S}^{n-1})\cup L(\log ^{+}L)^{1/2}(\text{S}^{n-1})$. Our main results represent improvements as well as natural extensions of many previously known results.

Keywords

Marcinkiewicz integralrough kernelsurfaces of revolutionTriebel–Lizorkin spaceBesov space

MSC classification

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 47G10: Integral operators
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 104 , Issue 3 , June 2018 , pp. 380 - 402
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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