Representability of Analytic Functions in Terms of Their Boundary Values

R. A. Aliyev

Matematičeskie zametki, Tome 73 (2003) no. 1, pp. 8-21

Résumé

Suppose that $\nu$ is an arbitrary finite complex Borel measure on the interval $[0;2\pi)$, $u(re^{i\varphi})$ is its Poisson integral, $v(re^{i\varphi})$ and $u(re^{i\varphi})$ are the conjugate harmonics of $F(z)=u(z)+iv(z)$, $z=re^{i\varphi}$ and $F(t)$ is the nontangential limiting value of the analytic function $F(z)$ as $z\to t=e^{i\theta}$. In this paper, we consider the problem of representing the analytic function $F(z)$ in terms of its boundary values $F(t)$ .