Abstract
In this paper we study the fractional Dirichlet p-sub-Laplacian in a Haar measurable set on homogeneous Lie groups. We show analogues of the fractional Sobolev and Hardy inequalities and we also present a Lyapunov-type inequality for the fractional p-sub-Laplacian. As a consequence of the Lyapunov-type inequality we obtain an estimate of the first eigenvalue in a quasi-ball for the Dirichlet fractional p-sub-Laplacian.
| Original language | English |
|---|---|
| Pages (from-to) | 435-452 |
| Number of pages | 18 |
| Journal | Advances in Operator Theory |
| Volume | 5 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - May 1 2020 |
Funding
The authors were supported in parts by the MESRK Grant AP05130981 and Nazarbayev University Program 091019CRP2120. Funding was provided by Nazarbayev University (KZ) (Grant no. NU FDCRG 09118FD5353). The authors were supported in parts by the MESRK Grant AP05130981 and Nazarbayev University Program 091019CRP2120. Funding was provided by Nazarbayev University (KZ) (Grant no. NU FDCRG 09118FD5353).
Keywords
- Fractional Hardy inequality
- Fractional p-sub-Laplacian
- Fractional Sobolev inequality
- Homogeneous Lie groups
- Lyapunov-type inequality
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory