The aim of this paper is to study singular integrals T generated by holomorphic kernels 𝛷 defined on a natural neighbourhood of the set ${zζ^{-1}: z, ζ ∈ 𝛤, z ≠ ζ}$, where 𝛤 is a star-shaped Lipschitz curve, $𝛤 ={ exp(iz) : z = x+iA(x), A' ∈ L^{∞}[-π,π], A(-π ) =A(π)}$. Under suitable conditions on F and z, the operators are given by (1) $TF(z)= p.v. ∫_𝛤 𝛷(zη^{-1})F(η)(dη/η).$ We identify a class of kernels of the stated type that give rise to bounded operators on $L^{2} (𝛤,|d𝛤|)$. We establish also transference results relating the boundedness of kernels on closed Lipschitz curves to corresponding results on periodic, unbounded curves.
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.