Littlewood-Paley-Stein functions for Schrödinger operators

2017/05/18 by El Maati Ouhabaz, Ouhabaz, El Maati
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math.AP

paper · pdf · doi:10.48550/arxiv.1705.06794

arxiv created 2017/05/18 · openalex publication_date 2017/05/18 · arxiv updated 2017/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study boundedness on L^p(R^d) of vertical Littlewood-Paley-Stein functions for Schrödinger operators -Δ+ V with nonnegative potential V. These functions are proved to be bounded on L^p for all p ∈ (1, 2]. The situation for p > 2 is different. We prove for a class of potentials that the boundedness on L^p for some p > d holds if and only if V= 0.

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