Vol. 2, No. 3, 2020

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$L^p$ estimates for Baouendi–Grushin operators

Giorgio Metafune, Luigi Negro and Chiara Spina

Vol. 2 (2020), No. 3, 603–625
Abstract

We prove Lp estimates for the Baouendi–Grushin operator Δx + |x|αΔy in Lp(N+M), 1 < p < , where x N , y M . When p = 2 more general weights belonging to the reverse Hölder class B2(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