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