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The Maximal Operator in Variable Spaces πΏ π(Β·)(Ξ©, Ο) with Oscillating Weights
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Vakhtang Kokilashvili
Published/Copyright:
March 10, 2010
Abstract
We study the boundedness of the maximal operator in the spaces πΏ π(Β·)(Ξ©, Ο) over a bounded open set Ξ© in π
π with the weight , where π€π has the property that
belongs to a certain Zygmund-type class. Weight functions π€π may oscillate between two power functions with different exponents. It is assumed that the exponent π(π₯) satisfies the DiniβLipschitz condition. The final statement on the boundedness is given in terms of index numbers of functions π€π (similar in a certain sense to the Boyd indices for the Young functions defining Orlicz spaces).
Key words and phrases:: Maximal functions; weighted Lebesgue spaces; variable exponent; potential operators
Received: 2005-07-08
Published Online: 2010-03-10
Published in Print: 2006-March
Β© Heldermann Verlag
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Keywords for this article
Maximal functions;
weighted Lebesgue spaces;
variable exponent;
potential operators
Articles in the same Issue
- A Common Fixed Point Theorem Connected to a Result of V. Popa and H. K. Pathak
- Holomorphic Vector Bundles on Holomorphically Convex Complex Manifolds
- Controllability of Sobolev Type Semilinear Functional Differential and Integrodifferential Inclusions with an Unbounded Delay
- Fixed Point Techniques and Stability for Neutral Nonlinear Differential Equations with Unbounded Delays
- Solution of a Nonclassical Problem of Oscillation of Two-Component Mixtures
- On the Fourier Expansions of Eisenstein Series of Some Types
- On the Full Transitivity of a Cotorsion Hull
- On Generating Relations Involving Generalized Gegenbauer Polynomials
- On Some Mutual Positions of Hyperplanes in a Finite-Dimensional Affine Space
- The Maximal Operator in Variable Spaces πΏ π(Β·)(Ξ©, Ο) with Oscillating Weights
- A Rational Model for the Evaluation Map
- The Pseudo-Spectral Collocation Method for Resonant Long-Short Nonlinear Wave Interaction
- A Vector-Valued Sharp Maximal Inequality on Morrey Spaces with Non-Doubling Measures
- A Noether Theorem on Unimprovable Conservation Laws for Vector-Valued Optimization Problems in Control Theory
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