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Title
A Progress in the Theory of Lebesgue Spaces with Variable Exponent: Singular Operators and Sobolev Theorem for Potentials

Abstract
The talk provides a discussion of recent results for the generalized Lebesgue spaces with variable exponent p(x) (GLSVE) including some results on boundedness of Hardy-Littlewood maximal operator and criterion for the weighted singular operator (with a power weight) to be bounded in such spaces. This result is applied to "localize" the Gohberg-Krupnik criterion of Fredholmness of singular integral operators in such spaces on Lyapunov curves. Some abstract Banach space reformulation of the Gohberg-Krupnik scheme of investigation of Fredholmness is given, from which the result for GLSVE, in particular follows due to the boundedness criterion for the weighted singular operator.

Speaker(s)
Stefan Samko (Universidade do Algarve)

Date
November 28, 2003

Time
14.30

Room
Room 5.5

 
     
 

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