Local Exponential Estimates for h-Pseudo-Differential Operators with Operator-Valued Symbols

Rabinovich, Vladimir

doi:10.1007/978-3-0348-0049-5_10

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Introduction and Main Results1

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2021

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“…Furthermore, by using h-pseudodifferential operator, the Cauchy problem of semiclassical elliptic partial differential equations is studied in [3][4][5]. Because of these operators importance, many scholars have studied one; see, for example, [6][7][8][9][10][11][12] and the references given there. Now, we consider the h-pseudodifferential operator as follows:…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

On $L^{2}$ -Boundedness of $h$ -Pseudodifferential Operators

Yang

2021

Journal of Function Spaces

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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 .

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