scholarly journals Hardy spaces of general Dirichlet series — a survey

2019 ◽  
Vol 119 ◽  
pp. 123-149 ◽  
Author(s):  
Andreas Defant ◽  
Ingo Schoolmann
Keyword(s):  
Dirichlet Series ◽  
Hardy Spaces ◽  
General Dirichlet Series

Hardy–Orlicz Spaces of Dirichlet Series: An Interpolation Problem on Abscissae of Convergence

2019 ◽  
Author(s):  
Maxime Bailleul ◽  
Pascal Lefèvre ◽  
Luis Rodríguez-Piazza
Keyword(s):  
Dirichlet Series ◽  
Hardy Spaces ◽  
Upper Bound ◽  
Interpolation Problem ◽  
Orlicz Spaces ◽  
Elementary Method ◽  
Abscissa Of Convergence ◽  
Upper Bound Estimate

Abstract The study of Hardy spaces of Dirichlet series denoted by $\mathscr{H}^p$ ($p\geq 1$) was initiated in [7] when $p=2$ and $p=\infty $, and in [2] for the general case. In this paper we introduce the Orlicz version of spaces of Dirichlet series $\mathscr{H}^\psi $. We focus on the case $\psi =\psi _q(t)=\exp (t^q)-1,$ and we compute the abscissa of convergence for these spaces. It turns out that its value is $\min \{1/q\,,1/2\}$ filling the gap between the case $\mathscr{H}^\infty $, where the abscissa is equal to $0$, and the case $\mathscr{H}^p$ for $p$ finite, where the abscissa is equal to $1/2$. The upper-bound estimate relies on an elementary method that applies to many spaces of Dirichlet series. This answers a question raised by Hedenmalm in [6].

scholarly journals Variants of a theorem of Helson on general Dirichlet series

2020 ◽  
Vol 279 (5) ◽  
pp. 108569 ◽  
Author(s):  
Andreas Defant ◽  
Ingo Schoolmann
Keyword(s):  
Dirichlet Series ◽  
General Dirichlet Series

A discrete universality theorem for general Dirichlet series

Analysis ◽  
2006 ◽  
Vol 26 (3) ◽  
Author(s):  
Renata Macaitiene
Keyword(s):  
Dirichlet Series ◽  
General Dirichlet Series ◽  
Universality Theorem ◽  
Discrete Universality

We prove a discrete universality theorem for functions given by general Dirichlet series, satisfying several conditions.

scholarly journals Vector-valued general Dirichlet series

2020 ◽  
Author(s):  
Daniel Carando ◽  
Andreas Defant ◽  
Felipe Marceca ◽  
Ingo Schoolmann
Keyword(s):  
Dirichlet Series ◽  
General Dirichlet Series ◽  
Vector Valued
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