Multipliers for logarithmic Cauchy integrals in the ball

E. S. Dubtsov

Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 40, Tome 370 (2009), pp. 44-57

Résumé

Let $B_n$ denote the unit ball in $\mathbb C^n$, $n\ge1$. Let $\mathcal K_0(n)$ denote the class of functions defined for $z\in B_n$ as a constant plus the integral of the kernel $\log(1/(1-\langle z,\zeta\rangle))$ against a complex Borel measure on the sphere $\{\zeta\in\mathbb C^n\colon|\zeta|=1\}$. We study properties of the holomorphic functions $g$ such that $fg\in\mathcal K_0(n)$ for all $f\in\mathcal K_0(n)$. Also, we investigate extended Cesàro operators on the spaces $\mathcal K_0(n)$, $n\ge1$. Bibl. – 15 titles.