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Growth Properties And Sequences Of Zeros Of Analytic Functions In Spaces Of Dirichlet Type

Daniel Girela Alvarez, José Angel Peláez Márquez
Published 2006 · Mathematics
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For 0 < p < 1 ,w e let p p 1 denote the space of those functions f that are analytic in the unit disc 1 Df z 2 C Vj zj < 1g and satisfy R 1 .1 j zj/ p 1 j f 0 .z/j p dx d y< 1. The spaces p p 1 are closely related to Hardy spaces. We have, p p 1 H p ,i f 0< p 2, and H p p p 1 ,i f 2 p < 1 .I n this paper we obtain a number of results about the Taylor coefficients of p p 1-functions and sharp estimates on the growth of the integral means and the radial growth of these functions as well as information on their zero sets.
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