Lp$L^p$‐boundedness properties for some harmonic analysis operators defined by resolvents for a Laplacian with drift in Euclidean spaces

Jorge J. Betancor, Juan C. Fariña and Lourdes Rodríguez‐Mesa

Mathematische Nachrichten, 2025, vol. 298, issue 3, 849-870

Abstract: We consider the Laplacian with drift in Rn$\mathbb {R}^n$ defined by Δν=∑i=1n(∂2∂xi2+2νi∂∂xi)$\Delta _\nu = \sum _{i=1}^n(\frac{\partial ^2}{\partial x_i^2} + 2 \nu _i\frac{\partial }{\partial {x_i}})$ where ν=(ν1,…,νn)∈Rn∖{0}$\nu =(\nu _1,\ldots ,\nu _n)\in \mathbb {R}^n\setminus \lbrace 0\rbrace$. This operator is self‐adjoint with respect to the locally doubling measure dμν(x)=e2⟨ν,x⟩dx$d\mu _\nu (x)=e^{2\langle \nu,x\rangle }dx$. We analyze the boundedness on Lp(Rn,μν)$L^p(\mathbb {R}^n,\mu _\nu)$, 1≤p 0={tk∂tk(I−tΔν)−M}t>0$\lbrace A^k_{\nu,M,t}\rbrace _{t>0}=\lbrace t^k\partial ^k_t(I-t\Delta _\nu)^{-M}\rbrace _{t>0}$, where M>0$M>0$ and k∈N$k\in \mathbb {N}$.

Date: 2025
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