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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 .

journal of function spaces

On <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msup> <mrow> <mi>L</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msup> </math>-Boundedness of <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>h</mi> </math>-Pseudodifferential Operators

On L 2 -Boundedness of h -Pseudodifferential Operators

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