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Boundedness of weighted singular integral operators in grand Lebesgue spaces
-
Vakhtang Kokilashvili
and
Stefan Samko
Published/Copyright:
June 6, 2011
Abstract
We obtain the necessary and sufficient conditions for the boundedness of the weighted singular integral operator with power weights in grand Lebesgue spaces. Because of applications to singular integral equations, the underlying set on which the functions are defined is a Carleson curve in the complex plane. Note that weighted boundedness of an operator in grand Lebesgue space is not the same as the boundedness in weighted grand Lebesgue space.
Keywords.: Grand Lebesgue space; weighted singular integral; boundedness; Carleson curve; singular integral equation; Fredholmness
Received: 2010-10-10
Published Online: 2011-06-06
Published in Print: 2011-June
© de Gruyter 2011
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Keywords for this article
Grand Lebesgue space;
weighted singular integral;
boundedness;
Carleson curve;
singular integral equation;
Fredholmness
Articles in the same Issue
- Polynomial approximation of functions in weighted Lebesgue and Smirnov spaces with nonstandard growth
- On the logarithmic summability of Fourier series
- On a relationship between absolutely nonmeasurable functions and Sierpiński–Zygmund functions
- Boundedness of weighted singular integral operators in grand Lebesgue spaces
- A generalization of the Euler beta function and applications
- Normality and shared values concerning differential polynomial
- Fixed point theorems for singlevalued and multivalued generalized contractions in metric spaces endowed with a graph
- About some geometric characteristics of the generalized Möbius–Listing surfaces
- Variation formulas of solution for a delay differential equation taking into account delay perturbation and the continuous initial condition
- An admissibility for topological degree of variable Besov and Triebel–Lizorkin spaces
- Boundedness of linear operators via atoms on Hardy spaces with non-doubling measures
