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Best constants in some operator smoothness estimates

Simon, Barry (1992) Best constants in some operator smoothness estimates. Journal of Functional Analysis, 107 (1). pp. 66-71. ISSN 0022-1236. doi:10.1016/0022-1236(92)90100-W.

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We provide a short proof of the inequality (cf. Ben-Artzi and Klainerman [Regularity and decay of evolution equations, preprint] and Kato and Yajima [Rev. Math. Phys. 1 (1989), 481–496]) ∝−∞^∞∥(1 + x^2)^(−12)(1 − Δ)^(14)e^(itΔ)u∥^2dt ⩽ C ∥u∥^2 with explicit (essentially exact) values for C.

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Simon, Barry0000-0003-2561-8539
Additional Information:© 1992 Elsevier Inc. Received 25 March 1991. Communicated by L. Gross. I thank M. Ben-Artzi for a useful conversation.
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Record Number:CaltechAUTHORS:20170905-100002232
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Official Citation:Barry Simon, Best constants in some operator smoothness estimates, Journal of Functional Analysis, Volume 107, Issue 1, 1992, Pages 66-71, ISSN 0022-1236, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81129
Deposited By: Ruth Sustaita
Deposited On:05 Sep 2017 18:46
Last Modified:15 Nov 2021 19:41

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