Havin-Mazya type uniqueness theorem for Dirichlet spacesReport as inadecuate




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1 LAA - Laboratoire Analyse et Applications URAC-03 2 IMB - Institut de Mathématiques de Bordeaux

Abstract : Let µ be a positive finite Borel measure on the unit circle. The associated Dirichlet space Dµ consists of holomorphic functions on the unit disc whose derivatives are square integrable when weighted against the Poisson integral of µ. We give a sufficient condition on a Borel subset E of the unit circle which ensures that E is a uniqueness set for Dµ. As application, we give an example of positive measure µ and a countable closed set E such that µE = 0 and E is uniqueness set for Dµ.

Keywords : uniqueness set weighted Dirichlet spaces capacity





Author: Hafid Bahajji-El Idrissi - Omar El-Fallah - Karim Kellay -

Source: https://hal.archives-ouvertes.fr/



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