Vekua’s Generalized Singular Integral on Carleson Curves in Weighted Variable Lebesgue Spaces
For a Carleson curve Γ we establish the boundedness, in weighted Lebesgue spaces L p(·)(Γ, ϱ) with variable exponent p(·), of the generalized singular integral operator which arises in the theory of I.N.Vekua generalized analytic functions. The obtained result is an extension of the known results even in the case of constant p. We also show that Vekua’s generalized singular integral exists a.e. for f ∈ L 1(Γ) on an arbitrary rectifiable curve.
Keywordssingular integrals generalized analytic functions weighted Lebesgue spaces variable exponent Carleson curve Zygmund conditions Bary-Stechkin class
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