Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves | Zendy

Karlovich Alexei Yu. | Zendy

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Maximal operators on variable Lebesgue spaces with weights related to oscillations of Carleson curves

Author(s) -

Karlovich Alexei Yu.

Publication year - 2010

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200810295

Subject(s) - mathematics , lp space , maximal operator , operator (biology) , class (philosophy) , lebesgue integration , pure mathematics , mathematical analysis , variable (mathematics) , point (geometry) , banach space , geometry , bounded function , biochemistry , chemistry , repressor , transcription factor , artificial intelligence , computer science , gene

We prove sufficient conditions for the boundedness of the maximal operator on variable Lebesgue spaces with weights φ t,γ ( τ ) = |( τ – t ) γ |, where γ is a complex number, over arbitrary Carleson curves. If the curve has different spirality indices at the point t and γ is not real, then φ t,γ is an oscillating weight lying beyond the class of radial oscillating weights considered recently by V. Kokilashvili, N. Samko, and S. Samko (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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