Atomic Characterizations of Hardy Spaces Associated to Schrödinger Type Operators

2018/11/29 by Zhang, Junqiang, Liu, Zongguang
#35J10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Primary 42B30 #Secondary 42B35

paper · doi:10.48550/arxiv.1811.12820

Abstract

In this article, the authors consider the Schrödinger type operator L:=-\rm div(A∇)+V on ℝⁿ with n≥ 3, where the matrix A is symmetric and satisfies uniformly elliptic condition and the nonnegative potential V belongs to the reverse Hölder class RH_q(ℝⁿ) with q∈(n/2, ∞). Let p(⋅): ℝⁿ→(0, 1] be a variable exponent function satisfying the globally log-Hölder continuous condition. The authors introduce the variable Hardy space H_L^p(⋅)(ℝⁿ) associated to L and establish its atomic characterization. The atoms here are closer to the atoms of variable Hardy space H^p(⋅)(ℝⁿ) in spirit, which further implies that H^p(⋅)(ℝⁿ) is continuously embedded in H_L^p(⋅)(ℝⁿ).

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