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The Maximal Operator in Variable Spaces 饾惪 饾憹(路)(惟, 蟻) with Oscillating Weights
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Vakhtang Kokilashvili
Ver枚ffentlicht/Copyright:
10. M盲rz 2010
Abstract
We study the boundedness of the maximal operator in the spaces 饾惪 饾憹(路)(惟, 蟻) over a bounded open set 惟 in 饾憛饾憶 with the weight , where 饾懁饾憳 has the property that
belongs to a certain Zygmund-type class. Weight functions 饾懁饾憳 may oscillate between two power functions with different exponents. It is assumed that the exponent 饾憹(饾懃) satisfies the Dini鈥揕ipschitz condition. The final statement on the boundedness is given in terms of index numbers of functions 饾懁饾憳 (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
漏 Heldermann Verlag
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- Controllability of Sobolev Type Semilinear Functional Differential and Integrodifferential Inclusions with an Unbounded Delay
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Schlagw枚rter f眉r diesen Artikel
Maximal functions;
weighted Lebesgue spaces;
variable exponent;
potential operators
Artikel in diesem Heft
- 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 饾惪 饾憹(路)(惟, 蟻) 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
- Weighted Inequalities for Integral Operators with Almost Homogeneous Kernels
- On the Convolution of Functions of Generalized Bounded Variations