Sharp endpoint estimates for some operators associated with the Laplacian with drift in Euclidean space

2017/01/18 by Hong-Quan Li, Li, Hong-Quan, Peter Sjögren +1
Mathematics · #42B25 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 42B20 #Secondary 58J35 #math.CA #msc:42B20 #msc:42B25 #msc:58J35

paper · pdf · doi:10.48550/arxiv.1701.04936

arxiv created 2017/01/18 · openalex publication_date 2017/01/18 · arxiv updated 2017/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let v ≠ 0 be a vector in \Rⁿ. Consider the Laplacian on \Rⁿ with drift Δ_v = Δ+ 2v⋅ ∇ and the measure dμ(x) = e^{2 ⟨ v, x ⟩} dx, with respect to which Δ_v is self-adjoint. This measure has exponential growth with respect to the Euclidean distance. We study weak type (1, 1) and other sharp endpoint estimates for the Riesz transforms of any order, and also for the vertical and horizontal Littlewood-Paley-Stein functions associated with the heat and the Poisson semigroups.

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