Papers by José Jorge Bueno Contreras
Journal of Mathematical Analysis and Applications, 2019
We consider the space H(ces p) of all Dirichlet series whose coefficients belong to the Cesàro se... more We consider the space H(ces p) of all Dirichlet series whose coefficients belong to the Cesàro sequence space ces p , consisting of all complex sequences whose absolute Cesàro means are in p , for 1 < p < ∞. It is a Banach space of analytic functions, for which we study the maximal domain of analyticity and the boundedness of point evaluations. We identify the algebra of analytic multipliers on H(ces p) as the Wiener algebra of Dirichlet series shifted to the vertical half-plane C 1/q := {s ∈ C : s > 1/q}, where 1/p + 1/q = 1. ✩ The authors acknowledge the support of MTM2015-65888-C4-1-P, MINECO (Spain). ✩✩ This work is part of the PhD thesis of José Jorge Bueno Contreras, defended in the University of Sevilla under the direction of Guillermo P. Curbera and Olvido Delgado.
In Chapter 3 we look into the multiplier algebra M(H(ces p )) of H(ces p ), that is, the space of... more In Chapter 3 we look into the multiplier algebra M(H(ces p )) of H(ces p ), that is, the space of all analytic functions f (on some domain containing C 1/q ) such that f g ∈ H(ces p ) for all g ∈ H(ces p ). The chapter is organized in four sections. In the first section we review general results for the multiplier algebra M(E) of a space E of Dirichlet series. The second section is devoted to the study of the multiplier algebra of the spaces A r (for which M(A r ) = A r ) study the existence of compact multipliers (Theorem 3.20) and the sequence multipliers from H(ces p ) into its multiplier algebra M(H(ces p )), that is, we study how "close" is H(ces p ) from M(H(ces p )) (Theorem 3.21). Chapter 4 is the last one. It contains a brief discussion concerning the Cesàro averaging operator C. The aim is to study the Cesàro averaging operator when acting on different spaces of Dirichlet series, via its action on the . The measurable functions which are bounded µ-a.e. form the Banach space L ∞ (Ω), which is endowed with the norm ∥f ∥ L ∞ (Ω) := ess sup ω∈Ω |f (ω)|.
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Papers by José Jorge Bueno Contreras