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The Riesz potential operator of variable order fi(x) is shown to be bounded from the Lebesgue space Lp(¢)(Rn) with variable exponent p(x) into the weighted space L q(¢) ‰ (R n ), where ‰ = (1 + jxj)¡∞ with some ∞ > 0 and 1 q(x) = 1 p(x) ¡ fi(x) n when p(x) is not necessarily constant at inflnity. It is as- sumed that the exponent p(x) satisfles the logarithmic continuity condition both locally and at inflnity and 1 < p(1) • p(x) • P < 1; x 2Rn.

On Sobolev Theorem for Riesz-Type Potentials in Lebesgue Spaces with Variable Exponent