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Weighted Sobolev theorem in Lebesgue spaces with variable exponent. (English) Zbl 1142.46018
This paper deals with Sobolev inequalities for Riesz potentials in variable exponent spaces with weights. The weights are radial and it is assumed that their growth is constrained by two polynomials of appropriate exponents. The variable exponent is $\log$-Hölder continuous, and the index $\alpha$ of the Riesz potential $I_\alpha$ is allowed to vary, as well.

MSC:
46E35Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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References:
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