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• W3105419231 abstract "Assuming that a Nash type inequality is satisfied by a non-negative self-adjoint operator <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we prove a Nash type inequality for the fractional powers <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A Superscript alpha> <mml:semantics> <mml:msup> <mml:mi>A</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>α<!-- α --></mml:mi> </mml:mrow> </mml:msup> <mml:annotation encoding=application/x-tex>A^{alpha }</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=upper A> <mml:semantics> <mml:mi>A</mml:mi> <mml:annotation encoding=application/x-tex>A</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Under some assumptions, we give ultracontractivity bounds for the semigroup <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=left-parenthesis upper T Subscript t comma alpha Baseline right-parenthesis> <mml:semantics> <mml:mrow> <mml:mo stretchy=false>(</mml:mo> <mml:msub> <mml:mi>T</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>α<!-- α --></mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo stretchy=false>)</mml:mo> </mml:mrow> <mml:annotation encoding=application/x-tex>(T_{t,{alpha }})</mml:annotation> </mml:semantics> </mml:math> </inline-formula> generated by <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=minus upper A Superscript alpha> <mml:semantics> <mml:mrow> <mml:mo>−<!-- − --></mml:mo> <mml:msup> <mml:mi>A</mml:mi> <mml:mrow class=MJX-TeXAtom-ORD> <mml:mi>α<!-- α --></mml:mi> </mml:mrow> </mml:msup> </mml:mrow> <mml:annotation encoding=application/x-tex>-A^{alpha }</mml:annotation> </mml:semantics> </mml:math> </inline-formula>." @default.
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• W3105419231 date "2007-01-25" @default.
• W3105419231 modified "2023-09-26" @default.
• W3105419231 title "Nash type inequalities for fractional powers of non-negative self-adjoint operators" @default.
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• W3105419231 doi "https://doi.org/10.1090/s0002-9947-07-04020-2" @default.
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