6 papers
Infinite dimensional systems of particles with interactions given by Dunkl operators
Andrei Velicu
Firstly we consider a finite dimensional Markov semigroup generated by Dunkl laplacian with drift terms. Using gradient bounds we show that for small coefficients this semigroup ha…
Logarithmic Sobolev inequalities for Dunkl operators with applications to functional inequalities for singular Boltzmann-Gibbs measures
Andrei Velicu
In this paper we study several inequalities of log-Sobolev type for Dunkl operators. After proving an equivalent of the classical inequality for the usual Dunkl measure , we a…
Spectral inequalities for a class of integral operators
Ari Laptev, Andrei Velicu
We obtain inequalities for the Riesz means for the discrete spectrum of a class of self-adjoint compact integral operators. Such bounds imply some inequalities for the counting fun…
Rellich, Gagliardo-Nirenberg, Trudinger and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applications
Andrei Velicu, Nurgissa Yessirkegenov
In this paper we obtain weighted higher order Rellich, weighted Gagliardo-Nirenberg, Trudinger, Caffarelli-Kohn-Nirenberg inequalities and the uncertainty principle for Dunkl opera…
Hardy-type inequalities for Dunkl operators with applications to many-particle Hardy inequalities
Andrei Velicu
In this paper we study various forms of the Hardy inequality for Dunkl operators, including the classical inequality, inequalities, an improved Hardy inequality, as well as t…
Sobolev-Type Inequalities for Dunkl Operators
Andrei Velicu
In this paper we study the Sobolev inequality in the Dunkl setting using two new approaches which provide a simpler elementary proof of the classical case , as well as an exte…