Boundedness of maximal operators and potential operators on Carleson curves in Lebesgue spaces with variable exponent |
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| Authors: | V Kokilashvili S Samko |
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| Institution: | (1) A. Razmadze Mathematical Institute, International Black Sea University, Georgia, Germany;(2) University of Algarve, Algarve, Portugal |
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| Abstract: | We prove the boundedness of the maximal operator ℳΓ in the spaces L
p(·)(Γ, ρ) with variable exponent p(t) and power weight ρ on an arbitrary Carleson curve under the assumption that p(t) satisfies the log-condition on Γ.
We prove also weighted Sobolev type L
p(·)(Γ, ρ) → L
q(·)(Γ, ρ)-theorem for potential operators on Carleson curves.
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| Keywords: | weighted generalized Lebesgue spaces variable exponent singular operator fractional integrals Sobolev theorem |
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