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June 2004 Lp estimates for rough parametric Marcinkiewicz integrals
H. M. Al-Qassem
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SUT J. Math. 40(2): 117-131 (June 2004). DOI: 10.55937/sut/1108749131


We prove the Lp boundedness of a class of parametric Marcinkiewicz integral operators Ω,hρ when h satisfies a certain integrability condition and Ω belongs to the block space Bq(0,1/2)(Sn1) for some q>1, n2. Also, we obtain the Lp boundedness for a class of rough parametric Marcinkiewicz integral operators Ω,h,λ*,ρ and Ω,h,Sρ related to the Littlewood-Paley gλ*-function and the area integral S, respectively. Our results are essential improvement and extension of some previously known results.


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H. M. Al-Qassem. "Lp estimates for rough parametric Marcinkiewicz integrals." SUT J. Math. 40 (2) 117 - 131, June 2004.


Received: 23 July 2004; Revised: 23 October 2004; Published: June 2004
First available in Project Euclid: 18 June 2022

Digital Object Identifier: 10.55937/sut/1108749131

Primary: 42B25 , 42B30

Keywords: Block space , Littlewood-Paley g-function , Lusin area integral , Marcinkiewicz integral , Rough kernel

Rights: Copyright © 2004 Tokyo University of Science

Vol.40 • No. 2 • June 2004
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