Integral means and boundary limits of Dirichlet series

  title={Integral means and boundary limits of Dirichlet series},
  author={Eero Saksman and Kristian Seip},
  journal={Bulletin of the London Mathematical Society},
  • E. Saksman, K. Seip
  • Published 4 December 2007
  • Mathematics
  • Bulletin of the London Mathematical Society
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… 
On the boundary behaviour of the Hardy spaces of Dirichlet series and a frame bound estimate
Abstract A range of Hardy-like spaces of ordinary Dirichlet series, called the Dirichlet–Hardy spaces ℋp, p ≧ 1, have been the focus of increasing interest among researchers following a paper of
Interpolation of Hardy spaces of Dirichlet series
Carlson's theorem for different measures
  • Meredith Sargent
  • Mathematics
    Journal of Mathematical Analysis and Applications
  • 2018
On generalized Hardy classes of Dirichlet series
We generalize the Hardy class H^2 of Dirichlet series studied by Hedenmalm, Lindqvist, Olofsson, Olsen, Saksman, Seip and others to consider more general Dirichlet series. We prove some results on
Contractive inequalities for Bergman spaces and multiplicative Hankel forms
We consider sharp inequalities for Bergman spaces of the unit disc, establishing analogues of the inequality in Carleman's proof of the isoperimetric inequality and of Weissler's inequality for
Fatou and brothers Riesz theorems in the infinite-dimensional polydisc
We study the boundary behavior of functions in the Hardy spaces on the infinite-dimensional polydisc. These spaces are intimately related to the Hardy spaces of Dirichlet series. We exhibit several
Dirichlet Series and Function Theory in Polydiscs
The interaction between Dirichlet series and function theory in polydiscs dates back to a fundamental insight of Harald Bohr and the subse- quent groundbreaking work on multilinear forms and
Fourier Multipliers for Hardy Spaces of Dirichlet Series
We obtain new results on Fourier multipliers for Dirichlet-Hardy spaces. As a consequence, we establish a Littlewood-Paley inequality, and we give a simple proof that the Dirichlet monomials form a


Hardy Spaces of Dirichlet Series and Their Composition Operators
Abstract. In [9], Hedenmalm, Lindqvist and Seip introduce the Hilbert space of Dirichlet series with square summable coefficients , and begin its study, with modern functional and harmonic analysis
Carleson's convergence theorem for Dirichlet series
A Hilbert space of Dirichlet series is obtained by considering the Dirichlet series f(s) = Sigma(n=1)(infinity) a(n)n(-s) that satisfy Sigma(n=0)(infinity) \a(n)\(2) 1/2 and define a functions tha ...
Dirichlet series and functional analysis
The study of Dirichlet series of the form \( \sum\nolimits_{n = 1}^\infty {a_n n^{ - s} } \) has a long history beginning in the nineteenth century, and the interest was due mainly to the central
Ten lectures on the interface between analytic number theory and harmonic analysis
Uniform distribution van der Corput sets Exponential sums I: The methods of Weyl and van der Corput Exponential sums II: Vinogradov's method An introduction to Turan's method Irregularities of
Analytic Number Theory
Introduction Arithmetic functions Elementary theory of prime numbers Characters Summation formulas Classical analytic theory of $L$-functions Elementary sieve methods Bilinear forms and the large
A Hilbert space of Dirichlet series and systems of dilated functions in $L^2(0,1)$
For a function $\varphi$ in $L^2(0,1)$, extended to the whole real line as an odd periodic function of period 2, we ask when the collection of dilates $\varphi(nx)$, $n=1,2,3,\ldots$, constitutes a
It is still unknown whether there are families of tight knots whose lengths grow faster than linearly with crossing numbers, but the largest power has been reduced to 3/z, and some other physical models of knots as flattened ropes or strips which exhibit similar length versus complexity power laws are surveyed.
Über die gleichmäßige Konvergenz Dirichletscher Reihen.
Einleitung. Es sei (1.) 0< 1< 2<·. .< <... (lim . = ) n=oo eine Folge reeller Zahlen und (2.) iane-» n=l eine zugehörige Dirichletsche Reihe, die ein Konvergenzgebiet besitzt. Dann existieren
The Legacy of Niels Henrik Abel
The collected works of Niels Henrik Abel, edited by Sophus Lie and Ludwig Sylow in 1881, contain 29 papers. The first was written in 1823 when Abel was 21 years old, and the last was jotted down on
Collected Mathematical Works’, Vol. I, Dirichlet Series and the Riemann Zeta-Function (Danish
  • Mathematical Society,
  • 1952