TY - JOUR
T1 - Hardy and Rellich inequalities, identities, and sharp remainders on homogeneous groups
AU - Ruzhansky, Michael
AU - Suragan, Durvudkhan
N1 - Funding Information:
The authors were supported in parts by the EPSRC grants EP/K039407/1 and EP/R003025/1, and by the Leverhulme Grant RPG-2014-02, as well as by the MESRK grant 5127/GF4. The second author was also supported by the Ministry of Science of the Russian Federation (the Agreement number 02.a03.21.0008).
Publisher Copyright:
© 2017 The Authors
PY - 2017/9/7
Y1 - 2017/9/7
N2 - We give sharp remainder terms of Lp and weighted Hardy and Rellich inequalities on one of most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups. As consequences, we obtain analogues of the generalised classical Hardy and Rellich inequalities and the uncertainty principle on homogeneous groups. We also prove higher order inequalities of Hardy–Rellich type, all with sharp constants. A number of identities are derived including weighted and higher order types.
AB - We give sharp remainder terms of Lp and weighted Hardy and Rellich inequalities on one of most general subclasses of nilpotent Lie groups, namely the class of homogeneous groups. As consequences, we obtain analogues of the generalised classical Hardy and Rellich inequalities and the uncertainty principle on homogeneous groups. We also prove higher order inequalities of Hardy–Rellich type, all with sharp constants. A number of identities are derived including weighted and higher order types.
KW - Homogeneous Lie group
KW - L-Hardy inequality
KW - Rellich inequality
KW - Uncertainty principle
KW - Weighted Hardy inequality
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U2 - 10.1016/j.aim.2017.07.020
DO - 10.1016/j.aim.2017.07.020
M3 - Article
AN - SCOPUS:85026226223
SN - 0001-8708
VL - 317
SP - 799
EP - 822
JO - Advances in Mathematics
JF - Advances in Mathematics
ER -