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Singular Integrals in Weighted Lebesgue Spaces with Variable Exponent
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V. Kokilashvili
Published/Copyright:
February 26, 2010
Abstract
In the weighted Lebesgue space with variable exponent the boundedness of the Calderón–Zygmund operator is established. The variable exponent 𝑝(𝑥) is assumed to satisfy the logarithmic Dini condition and the exponent β of the power weight ρ(𝑥) = |𝑥 – 𝑥0|β is related only to the value 𝑝(𝑥0). The mapping properties of Cauchy singular integrals defined on the Lyapunov curve and on curves of bounded rotation are also investigated within the framework of the above-mentioned weighted space.
Key words and phrases:: Variable exponent; singular integral operators; Lyapunov curve; curve of bounded rotation
Received: 2002-11-25
Published Online: 2010-02-26
Published in Print: 2003-March
© Heldermann Verlag
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Keywords for this article
Variable exponent;
singular integral operators;
Lyapunov curve;
curve of bounded rotation
Articles in the same Issue
- On One Theorem of S. Warschawski
- Investigation of Two-Dimensional Models of Elastic Prismatic Shell
- Branched Coverings and Minimal Free Resolution for Infinite-Dimensional Complex Spaces
- Operational Identities for Circular and Hyperbolic Functions and Their Generalizations
- Bi-Hamiltonian Structure as a Shadow of Non-Noether Symmetry
- On the Oscillation of Solutions of First Order Differential Equations with Retarded Arguments
- Combinatorial Homology in a Perspective of Image Analysis
- Internal Crossed Modules
- Cochain Operations Defining Steenrod ⌣𝑖-Products in the Bar Construction
- On Maximal 𝑜𝑡-Subsets of the Euclidean Plane
- Inversion of the Cauchy Integral Taken over the Double Periodic Line
- Singular Integrals in Weighted Lebesgue Spaces with Variable Exponent
- Local Growth of Weierstrass σ-Function and Whittaker-Type Derivative Sampling
- Sturm–Liouville and Focal Higher Order BVPs with Singularities in Phase Variables
- On Some Convexity Properties of Generalized Cesáro Sequence Spaces
