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Classes of weights related to Schrödinger operators

In this work we obtain boundedness on weighted Lebesgue spaces on R d of the semi-group maximal function, Riesz transforms, fractional integrals and g-function associated to the Schrödinger operator − Δ + V , where V satisfies a reverse Hölder inequality with exponent greater than d / 2 . We conside...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2011-01, Vol.373 (2), p.563-579
Main Authors: Bongioanni, B., Harboure, E., Salinas, O.
Format: Article
Language:English
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Summary:In this work we obtain boundedness on weighted Lebesgue spaces on R d of the semi-group maximal function, Riesz transforms, fractional integrals and g-function associated to the Schrödinger operator − Δ + V , where V satisfies a reverse Hölder inequality with exponent greater than d / 2 . We consider new classes of weights that locally behave as Muckenhoupt's weights and actually include them. The notion of locality is defined by means of the critical radius function of the potential V given in Shen (1995) [8].
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2010.08.008