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AuthorAl-Qassem, Hussain
AuthorPan, Yibiao
Available date2024-02-08T09:11:50Z
Publication Date2009-01-01
Publication NameCollectanea Mathematica
Identifierhttp://dx.doi.org/10.1007/BF03191206
CitationAl-Qassem, H., & Pan, Y. (2009). On certain estimates for Marcinkiewicz integrals and extrapolation. Collectanea mathematica, 60, 123-145.‏
ISSN00100757
URIhttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=76649104279&origin=inward
URIhttp://hdl.handle.net/10576/51672
AbstractWe obtain Lp estimates for parametric Marcinkiewicz integrals associated to polynomial mappings and with rough kernels on the unit sphere as well as on the radial direction. These estimates will allow us to use an extrapolation argument to obtain some new and improved results on Marcinkiewicz integrals. Also, such estimates provide us with a unifying approach in dealing with Marcinkiewicz integrals when the kernel function Ω belongs to the class of block spaces-B(0,α)q (Sn-1) aswell as when Ω belongs to the class L(log L)α(Sn-1). Our conditions on the kernels are known to be the best possible in their respective classes.© 2009 Universitat de Barcelona.
Languageen
PublisherUniversidad de Barcelona
SubjectBlock spaces
Extrapolation
L boundedness p
Marcinkiewicz integrals
Maximal functions
Rough kernel
TitleOn certain estimates for marcinkiewicz integrals and extrapolation
TypeArticle
Pagination123-145
Issue Number2
Volume Number60
dc.accessType Open Access


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