Coincidence of weighted Hardy spaces associated with higher-order Schrödinger operators

Abstract

Let k∈{1,2,3…}, d∈{2k+1,2k+2,…} and V∈RHσ∩Gk,d(−Δ)k with σ≥d/2. Here RHσ is a reverse Hölder class and Gk,d(−Δ)k is a Gaussian class associated with (−Δ)k. Let w∈A∞ρ. Consider the Schrödinger operator L1=−Δ+V and its higher-order counterpart L=(−Δ)k+Vk on their maximal domains. We show that the weighted Hardy spaces Hw,L11(Rd) and Hw,L1(Rd) coincide as normed spaces for certain k and V.