Geodesic
Representability of Analytic Functions in Terms of Their Boundary Values
Matematičeskie zametki, Tome 73 (2003) no. 1, pp. 8-21.

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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 $F(t)$ . 
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R. A. Aliyev. Representability of Analytic Functions in Terms of Their Boundary Values. Matematičeskie zametki, Tome 73 (2003) no. 1, pp. 8-21. http://geodesic.mathdoc.fr/item/MZM_2003_73_1_a1/

[1] Ulyanov P. L., “Ob $A$-integrale Koshi”, UMN, 11:5 (1956), 223–229 | MR | Zbl

[2] Vinogradova I. A., “Obobschennyi integral i sopryazhennye funktsii”, Matem. sb., 99 (141):1 (1976), 84–121 | MR

[3] Vinogradova I. A., “Ob $LG^*$-integrale tipa Koshi”, Matem. zametki, 20:5 (1976), 645–653 | MR | Zbl

[4] Riesz M., “Sur les fonctions conjuguees”, Math. Z., 27 (1927), 218–244 | DOI | MR

[5] Ulyanov P. L., “$A$-integral i sopryazhennye funktsii”, Uchenye zap. Mosk. un-ta, 181 (1956), 139–157 | MR

[6] Hruscev S. V., Vinogradov S. A., “Free interpolation in the space of uniformly convergent Taylor series”, Lect. Notes in Math., 864, 1981, 171–213 | MR

[7] Salimov T. S., “K teoreme E. Titchmarsha o sopryazhennoi funktsii”, Proceedings of A. Razmadze Math. Institute, 102 (1993), 99–114 | MR

[8] Kolmogorov A. N., Fomin S. V., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1989

[9] Garnett Dzh., Ogranichennye analiticheskie funktsii, Mir, M., 1984 | Zbl