ISHIGE, Kazuhiro; KABEYA, Yoshitsugu; OUHABAZ, El Maati

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ISHIGE, Kazuhiro
Tohoku University [Sendai]

KABEYA, Yoshitsugu
Osaka Prefecture University

OUHABAZ, El Maati
Institut de Mathématiques de Bordeaux [IMB]

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Proceedings of the London Mathematical Society. 2017

London Mathematical Society

Résumé en anglais

We consider the Schrödinger operator H = −∆ + V (|x|) with radial potential V which may have singularity at 0 and a quadratic decay at infinity. First, we study the structure of positive harmonic functions of H and give their precise behavior. Second, under quite general conditions we prove an upper bound for the correspond heat kernel p(x, y, t) of the type 0 < p(x, y, t) ≤ C t − N 2 U (min{|x|, √ t})U (min{|y|, √ t}) U (√ t) 2 exp − |x − y| 2 Ct for all x, y ∈ R N and t > 0, where U is a positive harmonic function of H. Third, if U 2 is an A 2 weight on R N , then we prove a lower bound of a similar type.< Réduire

Project ANR

Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013

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Institut de Mathématiques de Bordeaux (IMB) - UMR 5251