A characterization of Hardy spaces associated with certain Schr "odinger\n operators

2013/10/08 by Jacek Dziubański, Dziubański, Jacek, Jacek Zienkiewicz +1
Mathematics · #35J10 (primary) 42B35 (secondary) #42B30 #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1310.2262

openalex publication_date 2013/10/08 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

Let K_{t t>0} be the semigroup of linear operators generated by a\nSchr "odinger operator -L=\Δ - V(x) on mathbb R^d, d\≥ 3, where\nV(x)\≥ 0 satisfies \Δ^-1 V\∈ L^\∞. We say that an\nL¹-function f belongs to the Hardy space H¹_L if the maximal function\n mathcal M_L f(x) = \sup_t>0 |K_tf(x)| belongs to L¹( mathbb R^d) . We\nprove that the operator (-\Δ)^{1 slash 2} L^{-1 slash 2} is an\nisomorphism of the space H¹_L with the classical Hardy space H¹( mathbb\nR^d) whose inverse is L^{1 slash 2} (-\Δ)^{-1 slash 2}. As a corollary\nwe obtain that the space H¹_L is characterized by the Riesz transforms\nR_j=\(\∂)/(\∂ x_j)L^{-1 slash 2}.\n

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