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.
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The author is supported in part by N.S.F. grant DMS 9970151.
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Poltoratski, A. Images of non-tangential sectors under Cauchy transforms. J. Anal. Math. 89, 385–395 (2003). https://doi.org/10.1007/BF02893089
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DOI: https://doi.org/10.1007/BF02893089