Endpoint Estimates for a Class of Littlewood-Paley Operators with Nondoubling Measures | Zendy

Qingying Xue | Zendy; Juyang Zhang | Zendy

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Endpoint Estimates for a Class of Littlewood-Paley Operators with Nondoubling Measures

Author(s) -

Qingying Xue,

Juyang Zhang

Publication year - 2009

Publication title -

journal of inequalities and applications

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.735

H-Index - 50

eISSN - 1029-242X

pISSN - 1025-5834

DOI - 10.1155/2009/175230

Subject(s) - mathematics , standard probability space , lebesgue measure , measure (data warehouse) , corollary , bounded function , lebesgue–stieltjes integration , space (punctuation) , class (philosophy) , lebesgue integration , lp space , pure mathematics , lebesgue's number lemma , operator (biology) , discrete mathematics , mathematical analysis , banach space , operator theory , riemann integral , fourier integral operator , artificial intelligence , computer science , linguistics , philosophy , biochemistry , chemistry , repressor , database , transcription factor , gene

Let Open image in new window be a positive Radon measure on Open image in new window which may be nondoubling. The only condition that Open image in new window satisfies is Open image in new window Open image in new window for all Open image in new window , Open image in new window , and some fixed constant Open image in new window . In this paper, we introduce the operator Open image in new window related to such a measure and assume it is bounded on Open image in new window . We then establish its boundedness, respectively, from the Lebesgue space Open image in new window to the weak Lebesgue space Open image in new window , from the Hardy space Open image in new window to Open image in new window and from the Lesesgue space Open image in new window to the space Open image in new window . As a corollary, we obtain the boundedness of Open image in new window in the Lebesgue space Open image in new window with Open image in new window .

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