TY - JOUR
T1 - Hardy and Rellich inequalities for anisotropic p-sub-Laplacians
AU - Ruzhansky, M.
AU - Sabitbek, B.
AU - Suragan, D.
N1 - Funding Information:
M. Ruzhansky was supported by the EPSRC Grant EP/R003025/1, by the Leverhulme Research Grant RPG-2017-151, and by the FWO Odysseus Grant. B. Sabitbek was supported by the MESRK target program BR05236656 and the Nazarbayev University SPG Grant SST 2018040. D. Suragan was supported in parts by the Nazarbayev University SPG Grant. No new data was collected or generated during the course of this research.
Publisher Copyright:
© 2019, Tusi Mathematical Research Group (TMRG).
PY - 2020/4/1
Y1 - 2020/4/1
N2 - In this paper we establish the subelliptic Picone type identities. As consequences, we obtain Hardy and Rellich type inequalities for anisotropic p-sub-Laplacians which are operators of the form Lpf:=∑i=1NXi(|Xif|pi-2Xif),1i, i= 1 , … , N, are the generators of the first stratum of a stratified (Lie) group. Moreover, analogues of Hardy type inequalities with multiple singularities and many-particle Hardy type inequalities are obtained on stratified groups.
AB - In this paper we establish the subelliptic Picone type identities. As consequences, we obtain Hardy and Rellich type inequalities for anisotropic p-sub-Laplacians which are operators of the form Lpf:=∑i=1NXi(|Xif|pi-2Xif),1i, i= 1 , … , N, are the generators of the first stratum of a stratified (Lie) group. Moreover, analogues of Hardy type inequalities with multiple singularities and many-particle Hardy type inequalities are obtained on stratified groups.
KW - Anisotropic p-sub-Laplacian
KW - Hardy inequality
KW - Picone identity
KW - Rellich inequality
KW - Stratified group
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U2 - 10.1007/s43037-019-00011-7
DO - 10.1007/s43037-019-00011-7
M3 - Article
AN - SCOPUS:85079688763
SN - 1735-8787
VL - 14
SP - 380
EP - 398
JO - Banach Journal of Mathematical Analysis
JF - Banach Journal of Mathematical Analysis
IS - 2
ER -