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Images of non-tangential sectors under Cauchy transforms |
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| Authors: | Alexei?Poltoratski author-information" > author-information__contact u-icon-before" > mailto:alexei@math.tamu.edu" title=" alexei@math.tamu.edu" itemprop=" email" data-track=" click" data-track-action=" Email author" data-track-label=" " >Email author |
| Affiliation: | (1) Department of Mathematics, Texas A & M University, 77843 College Station, TX, USA |
| Abstract: | Let μ be a complex measure on the circle. We denote byPμ andQμ the Poisson and conjugate Poisson integrals of μ in the unit disk, respectively. In this note, we study the relative asymptotic growth ofPμ andQμ near the support of μ. In particular, we show that on μ-almost every radius,Qμ grows no faster thanPμ. We also discuss related questions on the boundary behavior of analytic functions. The author is supported in part by N.S.F. grant DMS 9970151. |
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