G. Dall’Ara

activity

20132026

most citedAn optimal multiplier theorem for Grushin operators in the plane, I

6 citations · 29 across the 23 of their papers we have counts for

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4 papers · 1 filter

math.AP2026

Obstructions to exact regularity of sublaplacians

Gian Maria Dall'Ara

Let $M$ be a closed manifold equipped with a collection of smooth real vector fields $X_{1}, \dots, X_{k}$ and a smooth measure $μ$ . Let $P := \sum_{j} X_{j}^{†} X_{j}$ be the associated…

math.AP2024

On generalized Dirichlet integrals in the smooth and in the o-minimal setting

Gian Maria Dall'Ara

Given a compact manifold $M$ equipped with smooth vector fields $X_{1}, \dots, X_{r}$ , we consider the generalized Dirichlet energy \[\mathbf{E}(f)= \sum_{j=1}^r\int_M |X_jf|^2\, dm,\]…

math.AP2021★ 6 cited

An optimal multiplier theorem for Grushin operators in the plane, I

Gian Maria Dall'Ara, Alessio Martini

Let $L = - \partial_{x}^{2} - V (x) \partial_{y}^{2}$ be the Grushin operator on $R^{2}$ with coefficient $V : R \to [0, \infty)$ . Under the sole assumptions that $V…

math.AP2017★ 5 cited

A robust approach to sharp multiplier theorems for Grushin operators

Gian Maria Dall'Ara, Alessio Martini

We prove a multiplier theorem of Mihlin-Hörmander type for operators of the form $- Δ_{x} - V (x) Δ_{y}$ on $R_{x}^{d_{1}} \times R_{y}^{d_{2}}$ , where $V(x) = \sum_{j=1}^{d_1}…