广义Campanato空间上粗糙核参数型Marcinkiewicz积分

Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (1): 154-166.

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Rough Parametric Marcinkiewicz Integrals on Generalized Campanato Spaces

ZHANG Song-Yan, TAO Xiang-Xing

Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023|Department of Mathematics, Ningbo University, Zhejiang Ningbo 315211

Received:2008-07-06 Revised:2009-09-30 Online:2010-01-01 Published:2010-01-01
Supported by:
国家自然科学基金(10771110, 10471069)资助.

Abstract

Abstract:

As a Littlewood-Paley function, let μ^ρ_{Ω, b}(f) be the parametric Marcinkiewicz integral with the rough kernel Ω∈L^q(S^n-1) satisfing the cancellation condition and integral Dini continuity, and the radial kernal b ∈?_s(R⁺)∩Θ_s(Rⁿ), 1<q, s<∞, and the parameter ρ ∈C with Re(ρ)>0. Under the only assumption of one point finiteness, the existence and boundedness of μ^ρ_{Ω, b}(f) on the generalized Campanato space L^p, φ(Rⁿ) are obtained. The theorems in this paper substantially extend early results.

Key words: Parametric Marcinkiewicz integral, Generalized Campanato space, Nonhomogeneous rough kernel, Existence and boundedness

CLC Number:

42B25

ZHANG Song-Yan, TAO Xiang-Xing. Rough Parametric Marcinkiewicz Integrals on Generalized Campanato Spaces[J].Acta mathematica scientia,Series A, 2010, 30(1): 154-166.

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Rough Parametric Marcinkiewicz Integrals on Generalized Campanato Spaces

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