Tohru Ozawa, Michael Ruzhansky, Durvudkhan Suragan
Published 2016-05-09Version 1
We prove $L^{p}$-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups, which is one of most general subclasses of nilpotent Lie groups, all with sharp constants. We also discuss some of their consequences. Already in the abelian case of $\mathbb{R}^{n}$ our results provide new insights in view of the arbitrariness of the choice of the not necessarily Euclidean quasi-norm.
Comments: 13 pages. arXiv admin note: substantial text overlap with arXiv:1603.06239
Sobolev inequalities, Euler-Hilbert-Sobolev and Sobolev-Lorentz-Zygmund spaces on homogeneous groups
On remainders and stability of anisotropic $L^{p}$-weighted Hardy inequalities
Spectral Gap Inequalities on Nilpotent Lie Groups in Infinite Dimensions
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