Area operators on Hardy spaces of Dirichlet series
Volume 285 / 2025
Studia Mathematica 285 (2025), 183-202
MSC: Primary 30B50; Secondary 47B38, 30H10
DOI: 10.4064/sm250223-15-7
Published online: 27 October 2025
Abstract
We introduce area operators $\mathbb A_{\mu ,l}$ in the Dirichlet series setting for $l \gt 0$ and positive Borel measures $\mu $ on the right half-plane $\mathbb C_0$. It is proved that if $\mu $ is a Carleson measure on $\mathbb C_0$, then for $0 \lt p \lt \infty $, the area operator $\mathbb A_{\mu ,l}$ is bounded from the Hardy space $\mathscr H^p_0$ of Dirichlet series vanishing at $+\infty $ to some $L^p$-space. We also give an application of our methods to Volterra operators.
