79 citations · 356 across the 65 of their papers we have counts for
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Anisotropic -weighted Hardy and -Caffarelli-Kohn-Nirenberg inequalities
Michael Ruzhansky, Durvudkhan Suragan
We establish sharp remainder terms of the -Caffarelli-Kohn-Niren\-berg inequalities on homogeneous groups, yielding the inequalities with best constants. Our methods also gi…
Sobolev type inequalities, Euler-Hilbert-Sobolev and Sobolev-Lorentz-Zygmund spaces on homogeneous groups
Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov
We define Euler-Hilbert-Sobolev spaces and obtain embedding results on homogeneous groups using Euler operators, which are homogeneous differential operators of order zero. Sharp r…
On horizontal Hardy, Rellich, Caffarelli-Kohn-Nirenberg and -sub-Laplacian inequalities on stratified groups
Michael Ruzhansky, Durvudkhan Suragan
In this paper, we present a version of horizontal weighted Hardy-Rellich type and Caffarelli-Kohn-Nirenberg type inequalities on stratified groups and study some of their consequen…
-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups
Tohru Ozawa, Michael Ruzhansky, Durvudkhan Suragan
We prove -Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups, which is one of most general subclasses of nilpotent Lie groups, all with sharp constants. We al…
Uncertainty relations on nilpotent Lie groups
Michael Ruzhansky, Durvudkhan Suragan
We give relations between main operators of quantum mechanics on one of most general classes of nilpotent Lie groups. Namely, we show relations between momentum and position operat…
On first and second eigenvalues of Riesz transforms in spherical and hyperbolic geometries
Michael Ruzhansky, Durvudkhan Suragan
In this note we prove an analogue of the Rayleigh-Faber-Krahn inequality, that is, that the geodesic ball is a maximiser of the first eigenvalue of some convolution type integral o…