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Zbl 1142.46018
Samko, N.G.; Samko, S.G.; Vakulov, B.G.
Weighted Sobolev theorem in Lebesgue spaces with variable exponent. (English)
[J] J. Math. Anal. Appl. 335, No. 1, 560-583 (2007). ISSN 0022-247X

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.
[Peter Hästö (Helsinki)]

MSC 2000:: *46E35 Sobolev spaces and generalizations

Keywords: Sobolev theorem; Hardy inequality; Lebesgue spaces with variable exponents; Riesz potentials; Spherical potentials; Zygmund--Bari--Stechkin conditions

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Zentralblatt MATH Berlin [Germany]