Integral means and boundary limits of Dirichlet series
By Eero Saksman, Kristian Seip. 2007
52 citations recorded by the source corpus.
This paper deals with the boundary behaviour of functions in the Hardy spaces ℋp for ordinary Dirichlet series. The main result, answering a question of Hedenmalm, shows that the classical Carlson theorem on integral means does not extend to the imaginary axis for functions in ℋ∞ , that is, for the ordinary Dirichlet series in H∞ of the right half‐plane. We discuss an important embedding problem for ℋp , the solution of which is only known when p is an even integer. Viewing ℋp as Hardy spaces of the infinite‐dimensional polydisc, we also present analogues of Fatou's theorem.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/946170b87785892f5dc4028789e92ad1a45b6a60
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In Applied Mathematics
- Kristian Seip
- Hervé Queffélec
- Alexandru Aleman
- Jan-Fredrik Olsen
- Adam J Harper
- Eero Saksman
- Fr'ed'eric Bayart
- S. Grivaux
Citations in the corpus
- Approximation numbers of composition operators on $H^p$ spaces of Dirichlet series (2014, background): “See [28] and also [19] for a thorough discussion of this inequality and its connections with Carleson measures.”
- MOMENTS OF RANDOM MULTIPLICATIVE FUNCTIONS, I: LOW MOMENTS, BETTER THAN SQUAREROOT CANCELLATION, AND CRITICAL MULTIPLICATIVE CHAOS (2017, background): “Theorem 1 also implies a negative answer to the so-called embedding problem for Dirichlet polynomials (see Question 2 of [24], or Problem 2.”
- Fourier Multipliers for Hardy Spaces of Dirichlet Series (2012, methodology): “(Note that the same argument can be made using only the Stone-Weierstrass theorem, see [11]) We define the subspace H(T) to consist of exactly these functions.”