Hausdorff operators on holomorphic Hardy spaces and applications

Abstract

The aim of this paper is to characterize the nonnegative functions $\phi$ defined on $(0,\infty )$ for which the Hausdorff operator $${\mathcal{H}}_{\phi }f(z)={\int }_0^{\infty }f\left(\frac{z}{t}\right)\frac{\phi (t)}{t}dt$$ is bounded on the Hardy spaces of the upper half-plane ${\mathcal{H}}_a^p({\mathbb{C}}_{+})$, $p\in [1,\infty ]$. The corresponding operator norms and their applications are also given.

Proc. Roy. Soc. Edinburgh Sect. A (to appear)

Cited by in corpus (1)

• Hausdorff Operators on Some Spaces of Holomorphic Functions on the Unit Disc