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- W2151154366 abstract "This work is concerned with extending the results of Calderón and Vaillancourt, proving the boundedness of Weyl pseudodifferential operators <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper O p Subscript h Superscript upper W e y l Baseline left-parenthesis upper F right-parenthesis> <mml:semantics> <mml:mrow> <mml:mi>O</mml:mi> <mml:msubsup> <mml:mi>p</mml:mi> <mml:mi>h</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>W</mml:mi> <mml:mi>e</mml:mi> <mml:mi>y</mml:mi> <mml:mi>l</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo stretchy=false>(</mml:mo> <mml:mi>F</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>Op_h^{Weyl} (F)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> in <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper L squared left-parenthesis double-struck upper R Superscript n Baseline right-parenthesis> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo stretchy=false>(</mml:mo> <mml:msup> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi mathvariant=double-struck>R</mml:mi> </mml:mrow> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>L^2({mathbb R}^n)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. We state conditions under which the norm of such operators has an upper bound independent of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=n> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding=application/x-tex>n</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. To this aim, we apply a decomposition of the identity to the symbol <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper F> <mml:semantics> <mml:mi>F</mml:mi> <mml:annotation encoding=application/x-tex>F</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, thus obtaining a sum of operators of a hybrid type, each of them behaving as a Weyl operator with respect to some of the variables and as an anti-Wick operator with respect to the other ones. Then we establish upper bounds for these auxiliary operators, using suitably adapted classical methods like coherent states." @default.
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- W2151154366 date "2014-12-22" @default.
- W2151154366 modified "2023-10-17" @default.
- W2151154366 title "On bounded pseudodifferential operators in a high-dimensional setting" @default.
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- W2151154366 doi "https://doi.org/10.1090/s0002-9939-2014-12379-3" @default.
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