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Sharp $L^p$ estimates for Schrödinger groups

Author:
D'Ancona, Piero   Nicola, Fabio   


Journal:
Revista Matemática Iberoamericana


Issue Date:
2016


Abstract(summary):

Consider a non-negative self-adjoint operator H in L-2 (R-d). We suppose that its heat operator e(-tH) satisfies an off-diagonal algebraic decay estimate, for some exponents p(0) is an element of [0, 2). Then we prove sharp L-p -> L-p frequency truncated estimates for the Schrodinger group e(itH) for p is an element of [p(0), p'(0)]. In particular, our results apply to every operator of the form H =3D (i del + A)(2) + V, with a magnetic potential A is an element of L-loc(2)(R-d, R-d) and an electric potential V whose positive and negative parts are in the local Kato class and in the Kato class, respectively.


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