A SOBOLEV TYPE THEOREM IN VARIABLE EXPONENT LEBESGUE SPACES WITH WEIGHTS IN SIGMUND - BARI - STECHKIN CLASS - Boris G. Vaculov; Natalia G. Samko; Stefan G. Samko (Современная наука и инновации)
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.