Local smoothing for Kato potentials in three dimensions

We prove weighted local smoothing estimates for the resolvent of the Laplacian in three dimensions with weights belonging to the Kerman–Sawyer class. This class contains the well‐known global Kato and Rollnik classes. We go on to discuss dispersive and Strichartz estimates for perturbations of the L...

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Bibliographic Details
Published in:Mathematische Nachrichten 2009-10, Vol.282 (10), p.1391-1405
Main Authors: Barceló, J. A., Bennett, J.M., Ruiz, A., Vilela, M. C.
Format: Article
Language:English
Subjects:
Schrödinger equations
smoothing estimates
weighted inequalities
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Summary:We prove weighted local smoothing estimates for the resolvent of the Laplacian in three dimensions with weights belonging to the Kerman–Sawyer class. This class contains the well‐known global Kato and Rollnik classes. We go on to discuss dispersive and Strichartz estimates for perturbations of the Laplacian by small potentials, and apply our results and observations to the well‐posedness in L2 of the Cauchy problem for some linear and semilinear Schrödinger equations (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
ISSN:0025-584X
1522-2616
DOI:10.1002/mana.200610808