On L2-Boundedness of h-Pseudodifferential Operators. (20th February 2021)

• Record Type: Journal Article
• Authors: Yang, Jie
• Other Names: Sun Wenchang Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-02-20
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/6690963
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : Let T a h be the h -pseudodifferential operators with symbol a . When a ∈ S ρ, 1 m and m = n ρ − 1 / 2, it is well known that T a h is not always bounded in L 2 ℝ n . In this paper, under the condition a x, ξ ∈ L ∞ S ρ n ρ − 1 / 2 ω, we show that T a h is bounded on L 2 .