In this paper, we establish Hardy inequalities of logarithmic type involving singularities on spheres in R<sup>n</sup> in terms of the Sobolev-Lorentz-Zygmund spaces. We prove it by absorbing singularities of functions on the spheres by subtracting the corresponding limiting values.
- best constant
- logarithmic Hardy inequality
- scaling invariant space
- Sobolev-Lorentz-Zygmund space
ASJC Scopus subject areas
- Applied Mathematics
- Discrete Mathematics and Combinatorics