H-p-Theory of General Dirichlet Series

摘要

Inspired by results of Bayart on ordinary Dirichlet series Sigma a(n)n(-s), the main purpose of this article is to start an Hp-theory of general Dirichlet series Sigma a(n)e(-lambda ns). Whereas the H-p-theory of ordinary Dirichlet series, in view of an ingenious identification of Bohr, may be seen as a sub-theory of Fourier analysis on the infinite dimensional torus T-infinity, the H-p-theory of general Dirichlet series is build as a sub-theory of Fourier analysis on certain compact abelian groups, including the Bohr compactification (R) over bar of the reals. Our approach allows to extend various important facts on Hardy spaces of ordinary Dirichlet series to the much wider setting of H-p-spaces of general Dirichlet series.