Boundedness of Generalized Parametric Marcinkiewicz Integrals Associated to Surfaces

Mohammed Ali and Oqlah Al-Refai
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Mohammed Ali: Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan
Oqlah Al-Refai: Department of Mathematics, Faculty of Science, Taibah University, Almadinah Almunawwarah 41477, Saudi Arabia

Mathematics, 2019, vol. 7, issue 10, 1-13

Abstract: In this article, the boundedness of the generalized parametric Marcinkiewicz integral operators M ? , ? , h , ? ( r ) is considered. Under the condition that ? is a function in L q ( S n ? 1 ) with q ? ( 1 , 2 ] , appropriate estimates of the aforementioned operators from Triebel–Lizorkin spaces to L p spaces are obtained. By these estimates and an extrapolation argument, we establish the boundedness of such operators when the kernel function ? belongs to the block space B q 0 , ? ? 1 ( S n ? 1 ) or in the space L ( log L ) ? ( S n ? 1 ) . Our results represent improvements and extensions of some known results in generalized parametric Marcinkiewicz integrals.

Keywords: L p boundedness; rough kernels; Marcinkiewicz integrals; Triebel–Lizorkin spaces; extrapolation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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