Singular integral operators on variable lebesgue spaces with radial oscillating weights

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8 Citations (Scopus)

Abstract

We prove a Fredholm criterion for operators in the Banach algebra of singular integral operators with matrix piecewise continuous coefficients acting on a variable Lebesgue space with a radial oscillating weight over a logarithmic Carleson curve. The local spectra of these operators are massive and have a shape of spiralic horns depending on the value of the variable exponent, the spirality indices of the curve, and the Matuszewska-Orlicz indices of the weight at each point. These results extend (partially) the results of A. Böttcher, Yu. Karlovich, and V. Rabinovich for standard Lebesgue spaces to the case of variable Lebesgue spaces.

Original languageEnglish
Title of host publicationOperator Algebras, Operator Theory and Applications - 18th International Workshop on Operator Theory and Applications, 2007
EditorsL.E. Labuschagne, J.J. Grobler, M. Möller
PublisherSpringer International Publishing
Pages185-212
Number of pages28
ISBN (Print)9783034601733
Publication statusPublished - 1 Jan 2010
Event18th International Workshop on Operator Theory and Applications, IWOTA 2007 - Potchefstroom, South Africa
Duration: 3 Jul 20076 Jul 2007

Publication series

NameOperator Theory: Advances and Applications
Volume195
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Conference

Conference18th International Workshop on Operator Theory and Applications, IWOTA 2007
Country/TerritorySouth Africa
CityPotchefstroom
Period3/07/076/07/07

Keywords

  • Carleson curve
  • Matuszewska-Orlicz indices
  • Radial oscillating weight
  • Submultiplicative function
  • Variable exponent
  • Variable Lebesgue space

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