1993/09/30 by Boris Korenblum, B. Korenblum, Korenblum, B. +3
Mathematics · #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Holomorphic and Operator Theory #math.CV #msc:32
paper · pdf · doi:10.48550/arxiv.math/9309202
arxiv created 1993/09/30 · arxiv updated 2009/11/30
We prove that there is a continuous non-negative function g on the unit sphere in \cd, d ≥ 2, whose logarithm is integrable with respect to Lebesgue measure, and which vanishes at only one point, but such that no non-zero bounded analytic function m in the unit ball, with boundary values m^⋆, has |m^⋆| ≤ g almost everywhere. The proof analyzes the common range of co-analytic Toeplitz operators in the Hardy space of the ball.