A note on Fourier multipliers on the product Hardy spaces

TL;DR

This paper investigates Fourier multipliers on product Hardy spaces, providing characterizations of multipliers between specific Hardy spaces and sequence or Lebesgue spaces, enhancing understanding of their boundedness properties.

Contribution

It offers new descriptions of Fourier multipliers from product Hardy spaces to sequence and Lebesgue spaces, expanding the theoretical framework for these operators.

Findings

Characterization of multipliers from H^1(𝕋×𝕋) to ℓ^2

Descriptions of multipliers from H^1(ℝ_+^2×ℝ_+^2) to L^1

Advances understanding of Fourier multiplier boundedness on product Hardy spaces

Abstract

In this article, we present some results about Fourier multipliers on Hardy spaces in the product case. We mainly give descriptions of multipliers from the space $H^1(\mathbb{T}\times\mathbb{T})$ into the space $\ell^2$ and from the space $H^1(\mathbb{R}_+^2\times\mathbb{R}_+^2)$ into the space $L^1$.