Schrödinger operators with reverse Hölder class potentials in the Dunkl setting and their Hardy spaces

2019/12/24 by Hejna, Agnieszka
#35J10 #35K08 #42B35 #FOS: Mathematics #Functional Analysis (math.FA) #primary: 42B30 #secondary: 42B25

paper · doi:10.48550/arxiv.1912.11352

Abstract

For a normalized root system R in \mathbb R^N and a multiplicity function k≥ 0 let \mathbf N=N+∑_{α∈ R} k(α). Let L=-Δ+V, V≥ 0, be the Dunkl--Schrödinger operator on \mathbb R^N. Assume that there exists q >max(1,(N)/(2)) such that V belongs to the reverse Hölder class RH^q(dw). We prove the Fefferman--Phong inequality for L. As an application, we conclude that the Hardy space H¹_L, which is originally defined by means of the maximal function associated with the semigroup e^tL, admits an atomic decomposition with local atoms in the sense of Goldberg, where their localization are adapted to V.

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