Marcinkiewicz Integrals on Weighted Weak Hardy Spaces

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2014 English Publisher:Hindawi LimitedJournal:Journal of Function Spaces, volume 2,014, pages 1-8 (issn: 2314-8896, eissn: 2314-8888,

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Authors: Yue Hu; Yueshan Wang;

doi: 10.1155/2014/765984

Marcinkiewicz Integrals on Weighted Weak Hardy Spaces

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Abstract

We prove that, under the conditionΩ∈Lipα, Marcinkiewicz integralμΩis bounded from weighted weak Hardy spaceWHwpRnto weighted weak Lebesgue spaceWLwpRnformaxn/n+1/2,n/n+α<p≤1, wherewbelongs to the Muckenhoupt weight class. We also give weaker smoothness condition assumed on Ω to imply the boundedness ofμΩfromWHw1ℝntoWLw1Rn.

Related Organizations

Jiaozuo University
China (People's Republic of)
Henan Polytechnic University
China (People's Republic of)

Keywords

Singular and oscillatory integrals (Calderón-Zygmund, etc.), Muckenhoupt weight class, Marcinkiewicz integral operator, QA1-939, Mathematics, \(H^p\)-spaces

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