TY - JOUR
T1 - Local properties of Hilbert spaces of Dirichlet series
AU - Olsen, Jan-Fredrik
PY - 2011
Y1 - 2011
N2 - We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This extends results recently obtained describing the local behavior of Dirichlet series with square summable coefficients in terms of local integrability, boundary behavior, Carleson measures and interpolating sequences. As these spaces can be identified with functions spaces on the infinite-dimensional polydisk, this gives new results on the Dirichlet and Bergman spaces on the infinite-dimensional polydisk, as well as the scale of Besov-Sobolev spaces containing the Drury-Arveson space on the infinite-dimensional unit ball. We use both techniques from the theory of sampling in Paley-Wiener spaces, and classical results from analytic number theory. (C) 2011 Elsevier Inc. All rights reserved.
AB - We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This extends results recently obtained describing the local behavior of Dirichlet series with square summable coefficients in terms of local integrability, boundary behavior, Carleson measures and interpolating sequences. As these spaces can be identified with functions spaces on the infinite-dimensional polydisk, this gives new results on the Dirichlet and Bergman spaces on the infinite-dimensional polydisk, as well as the scale of Besov-Sobolev spaces containing the Drury-Arveson space on the infinite-dimensional unit ball. We use both techniques from the theory of sampling in Paley-Wiener spaces, and classical results from analytic number theory. (C) 2011 Elsevier Inc. All rights reserved.
KW - Dirichlet series
KW - Hardy space in infinitely many complex variables
KW - Carleson measures
U2 - 10.1016/j.jfa.2011.07.007
DO - 10.1016/j.jfa.2011.07.007
M3 - Article
SN - 0022-1236
VL - 261
SP - 2669
EP - 2696
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 9
ER -