Hausdorff operators on holomorphic Hardy spaces and applications

Abstract

Abstract The aim of this paper is to characterize the non-negative functions φ defined on (0,∞) for which the Hausdorff operator $${\rm {\cal H}}_\varphi f(z) = \int_0^\infty f \left( {\displaystyle{z \over t}} \right)\displaystyle{{\varphi (t)} \over t}{\rm d}t$$ is bounded on the Hardy spaces of the upper half-plane ${\rm {\cal H}}_a^p ({\open C}_ + )$ , $p\in [1,\infty ]$ . The corresponding operator norms and their applications are also given.

Locations

• Proceedings of the Royal Society of Edinburgh Section A Mathematics - View
• arXiv (Cornell University) - View - PDF
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