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

We consider the Laplacian with drift in $R^n$ defined by ${\Delta }_{\nu }={\sum }_{i=1}^n(\frac{{\partial }^2}{\partial x_i^2}+2{\nu }_i\frac{\partial }{\partial x_i})$ where $\nu =({\nu }_1,\text{…},{\nu }_n)\in R^n\setminus \left\{0\right\}$. This operator is self-adjoint with respect to the locally doubling measure $d{\mu }_{\nu }\left(x\right)=e^{2⟨\nu ,x⟩}dx$. We analyze the boundedness on $L^p(R^n,{\mu }_{\nu })$, , of maximal operators, Littlewood–Paley functions, and variation and oscillation operators defined by the family ${\left\{A_{\nu ,M,t}^k\right\}}_{t>0}={\left\{t^k{\partial }_t^k{(I-t{\Delta }_{\nu })}^{-M}\right\}}_{t>0}$, where $M>0$ and $k\in N$.