23 citations · 48 across the 29 of their papers we have counts for
9 papers · 1 filter
Geometric Hardy and Hardy-Sobolev inequalities on Heisenberg groups
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper, we present the geometric Hardy inequality for the sub-Laplacian in the half-spaces on the stratified groups. As a consequence, we obtain the following geometric Hard…
Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups
Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan
In this note we prove the Stein-Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous nor…
Weighted anisotropic Hardy and Rellich type inequalities for general vector fields
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper, we establish the weighted anisotropic Hardy and Rellich type inequalities with boundary terms for general (real-valued) vector fields. As consequences, we derive new…
Anisotropic fractional Gagliardo-Nirenberg, weighted Caffarelli-Kohn-Nirenberg and Lyapunov-type inequalities, and applications to Riesz potentials and -sub-Laplacian systems
Aidyn Kassymov, Michael Ruzhansky, Durvudkhan Suragan
In this paper we prove the fractional Gagliardo-Nirenberg inequality on homogeneous Lie groups. Also, we establish weighted fractional Caffarelli-Kohn-Nirenberg inequality and Lyap…
Subelliptic geometric Hardy type inequalities on half-spaces and convex domains
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper we present and versions of the geometric Hardy inequalities in half-spaces and convex domains on stratified (Lie) groups. As a consequence, we obtain the…
A comparison principle for nonlinear heat Rockland operators on graded groups
Michael Ruzhansky, Durvudkhan Suragan
In this note we show a comparison principle for nonlinear heat Rockland operators on graded groups. We give a simple proof for it using purely algebraic relations. As an applicatio…