Hörmander Fourier multiplier theorems with optimal regularity in bi-parameter Besov spaces
type: Item
instance of: scholarly article
title: Hörmander Fourier multiplier theorems with optimal regularity in bi-parameter Besov spaces
zbMATH Open document ID: 1480.42017
author: Jiao Chen
author: Liang Huang
author: Guozhen Lu
published in: Mathematical Research Letters
publication date: 2021-11-30T00:00:00Z
review text: The paper under review is concerned with Fourier multipliers satisfying smoothness assumptions in bi-parameter Besov spaces. Main results are bi-parameter analogues of Hörmander-type multiplier theorems on Lebesgue spaces \(L^p(\mathbb{R}^{n_1} \times \mathbb{R}^{n_2})\) for \(1<p< \infty\) and on product Hardy spaces \(H^p(\mathbb{R}^{n_1} \times \mathbb{R}^{n_2})\) for \(0<p\leq 1\). These results improve earlier results for multipliers in bi-parameter Sobolev spaces. The sharpness of their bi-parameter Besov space assumptions is also obtained in the paper.
reviewed by: Jongchon Kim
Mathematics Subject Classification ID: 42B15
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 30H25
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 7435689
zbMATH Keywords: multiplier
zbMATH Keywords: bi-parameter Besov space
MaRDI profile type: Publication
DOI: 10.4310/MRL.2021.V28.N4.A4
description: scientific article; zbMATH DE number 7435689