Premium
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)