TY - JOUR
T1 - Lyapunov-type inequalities for the fractional p-sub-Laplacian
AU - Kassymov, Aidyn
AU - Suragan, Durvudkhan
N1 - Funding Information:
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).
Funding Information:
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).
Publisher Copyright:
© 2020, Tusi Mathematical Research Group (TMRG).
PY - 2020/5/1
Y1 - 2020/5/1
N2 - 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.
AB - 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.
KW - Fractional Hardy inequality
KW - Fractional p-sub-Laplacian
KW - Fractional Sobolev inequality
KW - Homogeneous Lie groups
KW - Lyapunov-type inequality
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U2 - 10.1007/s43036-019-00037-6
DO - 10.1007/s43036-019-00037-6
M3 - Article
AN - SCOPUS:85079829921
SN - 2538-225X
VL - 5
SP - 435
EP - 452
JO - Advances in Operator Theory
JF - Advances in Operator Theory
IS - 2
ER -