Fourier multipliers for Hardy spaces on Laguerre hypergroup

TL;DR

This paper establishes Fourier multiplier estimates for Hardy spaces on Laguerre hypergroups, providing atomic characterizations and extending Hormander's theorem to this setting.

Contribution

It introduces atomic and molecular characterizations of Hardy spaces on Laguerre hypergroups and proves a Hormander-type multiplier theorem for these spaces.

Findings

Fourier Laguerre transform estimates on Hardy spaces

Atomic and molecular characterizations of H^p spaces

Hormander's multiplier theorem extended to Laguerre hypergroups

Abstract

The main purpose of this paper is to give an estimate for the Fourier Laguerre transform on Hardy spaces in the setting of Laguerre hypergroup. The atomic and molecular characterization is investigated which allows us to prove a version of Hormander's multiplier theorem on H^p (0<p\leq1).