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Representability of Analytic Functions in Terms of Their Boundary Values

Authors:	Aliev R. A.

Affiliation:	(1) Baku State University, Russia

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

Keywords:	analytic function complex Borel measure Lebesgue measure Poisson integral Cauchy integral Hö lder continuity
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