Rough Marcinkiewicz integral operators

Hussain Al-Qassem and Ahmad Al-Salman

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 27, 1-9

Abstract:

We study the Marcinkiewicz integral operator M 𝒫 f ( x ) = ( ∫ − ∞ ∞ | ∫ | y | ≤ 2 t f ( x − 𝒫 ( y ) ) ( Ω ( y ) / | y | n − 1 ) d y | 2 d t / 2 2 t ) 1 / 2 , where 𝒫 is a polynomial mapping from ℝ n into ℝ d and Ω is a homogeneous function of degree zero on ℝ n with mean value zero over the unit sphere S n − 1 . We prove an L p boundedness result of M 𝒫 for rough Ω .

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:383721

DOI: 10.1155/S0161171201006548

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