, Volume 186, Issue 1, pp 95-107

Optimal heat kernel estimates for schrödinger operators with magnetic fields in two dimensions

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Abstract

Sharp smoothing estimates are proven for magnetic Schrödinger semigroups in two dimensions under the assumption that the magnetic field is bounded below by some positive constantB 0. As a consequence theL∞ norm of the associated integral kernel is bounded by theL∞ norm of the Mehler kernel of the Schrödinger semigroup with the constant magnetic fieldB 0.

© {dy1996} by the authors Reproduction of this article, in its entirety, by any means is permitted for noncommercial purposes
Work supported by N S F grant DMS-95-00840 and the Erwin Schrödinger Institute