Alessio Martini

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20232026

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4 papers · 1 filter

math.FA2026

Riesz transforms for the distinguished Laplacian on Damek-Ricci spaces and operator-valued multivariate spectral multipliers

Jie Liu, Alessio Martini

Let $Δ = \nabla^{*} \nabla$ be the distinguished Laplacian on a Damek-Ricci space. We prove the $L^{p}$ -boundedness of the vector of first-order Riesz transforms $\nabla Δ^{- 1/2}$ in…

math.FA2024

$L^{p}$ -boundedness of Riesz transforms on solvable extensions of Carnot groups

Alessio Martini, Paweł Plewa

Let $G = N ⋊ R$ , where $N$ is a Carnot group and $R$ acts on $N$ via automorphic dilations. Homogeneous left-invariant sub-Laplacians on $N$ and $R$ c…

math.FA2024

Singular integrals on $a x + b$ hypergroups and an operator-valued spectral multiplier theorem

Alessio Martini, Paweł Plewa

Let $L_{ν} = - \partial_{x}^{2} - (ν - 1) x^{- 1} \partial_{x}$ be the Bessel operator on the half-line $X_{ν} = [0, \infty)$ with measure $x^{ν - 1} d x$ . In this work we study singular inte…

math.FA2023

Riesz transform and spectral multipliers for the flow Laplacian on nonhomogeneous trees

Alessio Martini, Federico Santagati, Anita Tabacco +1

Let $T$ be a locally finite tree equipped with a flow measure $m$ . Let $L$ be the flow Laplacian on $(T, m)$ . We prove that the first order Riesz transform $\nabla \mathcal…

Riesz transforms for the distinguished Laplacian on Damek-Ricci spaces and operator-valued multivariate spectral multipliers

Lp-boundedness of Riesz transforms on solvable extensions of Carnot groups

Singular integrals on ax+b hypergroups and an operator-valued spectral multiplier theorem

Riesz transform and spectral multipliers for the flow Laplacian on nonhomogeneous trees

$L^{p}$ -boundedness of Riesz transforms on solvable extensions of Carnot groups

Singular integrals on $a x + b$ hypergroups and an operator-valued spectral multiplier theorem