On \(L^2\)-boundedness of \(h\)-pseudodifferential operators
type: Item
instance of: scholarly article
title: On \(L^2\)-boundedness of \(h\)-pseudodifferential operators
DOI: 10.1155/2021/6690963
author: Jie Yang
published in: Journal of Function Spaces
publication date: 2021-05-03T00:00:00Z
review text: Summary: Let \(T_a^h\) be the \(h\)-pseudodifferential operators with symbol \(a\). When \(a\in S_{\rho,1}^m\) and \(m=n (\rho -1)/2\), it is well known that \(T_a^h\) is not always bounded in \(L^2 (\mathbb{R}^n)\). In this paper, under the condition \(a(x,\xi) \in L^\infty S_\rho^{n(\rho -1)/2}(\omega)\), we show that \(T_a^h\) is bounded on \(L^2\).
Mathematics Subject Classification ID: 47G30
zbMATH DE Number: 7341758
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/6690963
OpenAlex ID: W3130367258
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description: scientific article; zbMATH DE number 7341758