A SOBOLEV TYPE THEOREM IN VARIABLE EXPONENT LEBESGUE SPACES WITH WEIGHTS IN SIGMUND - BARI - STECHKIN CLASS
Abstract
For the Riesz potential operator there are proved weighted estimates within the framework of weighted Lebesgue spaces with variable exponent. In case is a bounded do-main, the order potential is allowed to be variable as well. The weight functions are radial type functions «fixed» to a finite point and/or to infinity and have a typical feature of Muckenhoupt-Wheeden weights: they may oscillate between two power functions. Conditions on weights are given in terms of their Boyd-type indices. An analogue of such a weighted estimate is also obtained for spherical potential oper-ators on the unit sphere.
About the Authors
Boris G. Vaculov
Southern Federal University
Russian Federation
Russian Federation
Natalia G. Samko
Lulea University of Technology
Russian Federation
Russian Federation
Stefan G. Samko
Universidade do Algarve
Russian Federation
Russian Federation
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Review
For citations:
Vaculov B.G., Samko N.G., Samko S.G. A SOBOLEV TYPE THEOREM IN VARIABLE EXPONENT LEBESGUE SPACES WITH WEIGHTS IN SIGMUND - BARI - STECHKIN CLASS. Modern Science and Innovations. 2013;(3):33-39. (In Russ.)
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