Factorizations and Hardy–Rellich inequalities on stratified groups
Ruzhansky M. Yessirkegenov N.
2021European Mathematical Society Publishing House
Journal of Spectral Theory
2021#10Issue 41361 - 1411 pp.
In this paper, we obtain Hardy, Hardy–Rellich and refined Hardy inequalities on general stratified groups and weighted Hardy inequalities on general homogeneous groups using the factorization method of differential operators, inspired by the recent work of Gesztesy and Littlejohn [9]. We note that some of the obtained inequalities are new also in the usual Euclidean setting. We also obtain analogues of Gesztesy and Littlejohn’s 2-parameter version of the Rellich inequality on stratified groups and on the Heisenberg group, and a new two-parameter estimate on Rn which can be regarded as a counterpart to the Gesztesy and Littlejohn estimate. Moreover, we give some applications of Hardy and Rellich type inequalities to the lower semiboundedness and to form boundedness for interactions with countably many strong singularities on stratified groups.
Factorization , Hardy inequality , Hardy–Rellich inequality , Heisenberg group , Homogeneous Lie group , Stratified group
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Department of Mathematics: Analysis, Logic and Discrete Mathematics, Ghent University, Krijgslaan 281, Gent, 9000, Belgium
School of Mathematical Sciences, Queen Mary University of London, Mile End Rd, Stepney, London, E1 4NS, United Kingdom
Institute of Mathematics and Mathematical Modelling, Pushkina, 125, Almaty, 050010, Kazakhstan
Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, United Kingdom
Department of Mathematics: Analysis
School of Mathematical Sciences
Institute of Mathematics and Mathematical Modelling
Department of Mathematics
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