Remarks on L p -CKN Interpolation Inequalities of Hardy and Rellich Types on the Sphere
1 Department of Mathematics, University of Lagos, Akoka, Lagos State, Nigeria
2 University of Ilorin, Nigeria
3 Department of Mathematics and Computer Science, Tongling University, Tongling, 244000 Anhui, China
* Corresponding author: a.abolarinwa1@gmail.com
2 University of Ilorin, Nigeria
3 Department of Mathematics and Computer Science, Tongling University, Tongling, 244000 Anhui, China
* Corresponding author: a.abolarinwa1@gmail.com
Abstract
We prove a new family of L
p
-Caffarelli-Kohn-Nirenberg (CKN)
interpolation inequalities with sharp constants on the unit sphere
of dimension greater than or equal to two. Consequently, several
sharp Hardy type inequalities are obtained as special cases.
Moreover, the same method is adopted to establish a new class of
Hardy-Rellich type inequalities on the sphere, though, uncertain
whelther or not the constants in this case are optimal in general.
Keywords
Hardy-Rellich inequalities
Interpolation inequalities
Optimal constant
Laplacian
Geodesic distance
How to Cite
Abolarinwa, A., RAUF, K., & Yin, S. (2022). Remarks on L p -CKN Interpolation Inequalities of Hardy and Rellich Types on the Sphere. Nigerian Journal of Mathematics and Applications, 32(2), 1-13. https://doi.org/10.67897/njma.2022.x7af8ch8
A. Abolarinwa, K. RAUF, and S. Yin, "Remarks on L p -CKN Interpolation Inequalities of Hardy and Rellich Types on the Sphere," Nigerian Journal of Mathematics and Applications, vol. 32, no. 2, pp. 1-13, December 2022. doi: 10.67897/njma.2022.x7af8ch8
