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Rellich inequalities for sub-Laplacians with drift

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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 R-n, embedding the classical Rellich inequality into a family of Rellich inequalities with parameter dependent drifts.
Keywords
Sub-Laplacian, sub-Laplacians with drift, Rellich inequalities, stratified group, polarizable Carnot group, SPECTRAL MULTIPLIERS, HARDY, CONSTANTS

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Chicago
Ruzhansky, Michael, and Nurgissa Yessirkegenov. 2019. “Rellich Inequalities for sub-Laplacians with Drift.” Proceedings of the American Mathematical Society 147 (3): 1335–1349.
APA
Ruzhansky, M., & Yessirkegenov, N. (2019). Rellich inequalities for sub-Laplacians with drift. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 147(3), 1335–1349.
Vancouver
1.
Ruzhansky M, Yessirkegenov N. Rellich inequalities for sub-Laplacians with drift. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 2019;147(3):1335–49.
MLA
Ruzhansky, Michael, and Nurgissa Yessirkegenov. “Rellich Inequalities for sub-Laplacians with Drift.” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 147.3 (2019): 1335–1349. Print.
@article{8586227,
  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 R-n, embedding the classical Rellich inequality into a family of Rellich inequalities with parameter dependent drifts.},
  author       = {Ruzhansky, Michael and Yessirkegenov, Nurgissa},
  issn         = {0002-9939},
  journal      = {PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY},
  keywords     = {Sub-Laplacian,sub-Laplacians with drift,Rellich inequalities,stratified group,polarizable Carnot group,SPECTRAL MULTIPLIERS,HARDY,CONSTANTS},
  language     = {eng},
  number       = {3},
  pages        = {1335--1349},
  title        = {Rellich inequalities for sub-Laplacians with drift},
  url          = {http://dx.doi.org/10.1090/proc/14312},
  volume       = {147},
  year         = {2019},
}

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