Lp estimates for Baouendi–Grushin operators

We prove $L^{p}$ estimates for the Baouendi–Grushin operator $Δ_{x} + | x |^{α} Δ_{y}$ in $L^{p} (ℝ^{N + M})$ , $1 < p < \infty$ , where $x \in ℝ^{N}$ , $y \in ℝ^{M}$ . When $p = 2$ more general weights belonging to the reverse Hölder class $B_{2} (ℝ^{N})$ are allowed.

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Keywords

Baouendi–Grushin operators, degenerate elliptic equations, subelliptic equations, $L^p$ estimates

Mathematical Subject Classification 2010

Primary: 35H20, 35J70, 47F05

Milestones

Received: 27 November 2019

Revised: 24 January 2020

Accepted: 15 March 2020

Published: 17 November 2020

Authors

Giorgio Metafune
Dipartimento di Matematica “Ennio De Giorgi” Università del Salento Lecce Italy

Luigi Negro
Dipartimento di Matematica “Ennio De Giorgi” Università del Salento Lecce Italy

Chiara Spina
Dipartimento di Matematica “Ennio De Giorgi” Università del Salento Lecce Italy

Vol. 2, No. 3, 2020

Giorgio Metafune, Luigi Negro and Chiara Spina

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors