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Rellich inequalities for sub-Laplacians with drift


Authors: Michael Ruzhansky and Nurgissa Yessirkegenov
Journal: Proc. Amer. Math. Soc. 147 (2019), 1335-1349
MSC (2010): Primary 22E30, 43A80
DOI: https://doi.org/10.1090/proc/14312
Published electronically: December 6, 2018
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Abstract: In this note we prove horizontal weighted Rellich inequalities for the sub-Laplacian and for sub-Laplacians with drift on general stratified
groups. We show how the presence of a drift improves the known inequalities. Moreover, we obtain several versions of weighted Rellich inequalities for the sub-Laplacian with drift on the polarizable Carnot groups, also with the weights associated with the fundamental solution of the sub-Laplacian. The obtained results are already new for the Laplacian in the usual Euclidean setting of $ {\mathbb{R}}^n$, embedding the classical Rellich inequality into a family of Rellich inequalities with parameter dependent drifts.


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Additional Information

Michael Ruzhansky
Affiliation: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
Address at time of publication: Department of Mathematics, Ghent University, Belgium; and School of Mathematical Sciences, Queen Mary University of London, United Kingdom
Email: m.ruzhansky@imperial.ac.uk

Nurgissa Yessirkegenov
Affiliation: Institute of Mathematics and Mathematical Modelling, 125 Pushkin str., 050010 Almaty, Kazakhstan – and – Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
Email: n.yessirkegenov15@imperial.ac.uk

DOI: https://doi.org/10.1090/proc/14312
Keywords: Sub-Laplacian, sub-Laplacians with drift, Rellich inequalities, stratified group, polarizable Carnot group
Received by editor(s): September 15, 2017
Received by editor(s) in revised form: July 2, 2018
Published electronically: December 6, 2018
Additional Notes: The first author was supported in part by the EPSRC Grants EP/K039407/1 and EP/R003025/1, and by the Leverhulme Research Grant RPG-2017-151.
The second author was supported by the MESRK grant AP05133271. No new data was collected or generated during the course of research.
Communicated by: Michael Hitrik
Article copyright: © Copyright 2018 American Mathematical Society

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