On the factorization of bounded measurable functions in the classes of Cauchy type integrals with density from Lp(·)(Γ;ω)

Abstract

Let Γ be a simple rectifiable closed Carleson curve and be its measurable bounded nonzero function on Γ. It is proved in the paper that the factorization of such a function in the class of Cauchy type integrals with density from the Lebesgue space Lp(·)(Γ;ω) with variable exponent is equivalent to the property of the singular integral operator , where is the operator generated by a Cauchy singular operator, to be Noetherian in the space Lp(·)(Γ;ω). This result generalizes a theorem of I. B. Simonenko.