23 citations · 30 across the 7 of their papers we have counts for
7 papers
Isoperimetric inequalities for some integral operators arising in potential theory
Michael Ruzhansky, Durvudkhan Suragan
In this paper we review our previous isoperimetric results for the logarithmic potential and Newton potential operators. The main reason why the results are useful, beyond the intr…
Geometric maximizers of Schatten norms of some convolution type integral operators
Michael Ruzhansky, Durvudkhan Suragan
In this paper we prove that the ball is a maximizer of the Schatten -norm of some convolution type integral operators with non-increasing kernels among all domains of a given me…
Caffarelli-Kohn-Nirenberg and Sobolev type inequalities on stratified Lie groups
Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov
In this short paper, we establish a range of Caffarelli-Kohn-Nirenberg and weighted -Sobolev type inequalities on stratified Lie groups. All inequalities are obtained with s…
Weighted -Hardy and -Rellich inequalities with boundary terms on stratified Lie groups
Michael Ruzhansky, Bolys Sabitbek, Durvudkhan Suragan
In this paper, generalised weighted -Hardy,-Caffarelli-Kohn-Nirenberg, and -Rellich inequalities with boundary terms are obtained on stratified Lie groups. As conse…
Green's identities, comparison principle and uniqueness of positive solutions for nonlinear -sub-Laplacian equations on stratified Lie groups
Michael Ruzhansky, Durvudkhan Suragan
We propose analogues of Green's and Picone's identities for the -sub-Laplacian on stratified Lie groups. In particular, these imply a generalised Díaz-Saá inequality for the …
Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability, and superweights for -weighted Hardy inequalities
Michael Ruzhansky, Durvudkhan Suragan, Nurgissa Yessirkegenov
In this paper we give an extension of the classical Caffarelli-Kohn-Nirenberg inequalities: we show that for , with , $δ\in[0,1]\cap\left[\fra…