Rellich, Gagliardo-Nirenberg, Trudinger and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applications

DOI10.1007/s11856-021-2261-7OpenAlexW4200623176MaRDI QIDQ2143254

Nurgissa Yessirkegenov, Andrei Velicu

Publication date: 31 May 2022

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1904.08725

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Abstract harmonic analysis (43Axx)

Related Items (2)

A global existence result for a semilinear wave equation with lower order terms on compact Lie groups ⋮ Logarithmic Sobolev inequalities for Dunkl operators with applications to functional inequalities for singular Boltzmann-Gibbs measures

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analysis on \(h\)-harmonics and Dunkl transforms. Edited by Sergey Tikhonov
• Sobolev-type inequalities for Dunkl operators
• Trudinger type inequalities and uniqueness of weak solutions for the nonlinear Schrödinger mixed problem
• Riesz transform and Riesz potentials for Dunkl transform
• A transference theorem for the Dunkl transform and its applications
• Calogero-Moser-Sutherland models. Workshop, Centre de Recherches Mathématique, Montréal, Canada, March 10--15, 1997
• Nonlinear damped wave equations for the sub-Laplacian on the Heisenberg group and for Rockland operators on graded Lie groups
• Caffarelli-Kohn-Nirenberg and Sobolev type inequalities on stratified Lie groups
• On critical cases of Sobolev's inequalities
• Critical exponent of Fujita-type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity
• Best constants in Sobolev and Gagliardo-Nirenberg inequalities on graded groups and ground states for higher order nonlinear subelliptic equations
• Detailed proof of classical Gagliardo-Nirenberg interpolation inequality with historical remarks
• Riesz potential and maximal function for Dunkl transform
• The Hardy inequality and fractional Hardy inequality for the Dunkl Laplacian
• Limiting cases of Sobolev inequalities on stratified groups
• Fractional smoothness in \(L^p\) with Dunkl weight and its applications
• Extended Caffarelli-Kohn-Nirenberg inequalities and superweights for \(L^p\)-weighted Hardy inequalities
• Hardy inequalities on homogeneous groups. 100 years of Hardy inequalities
• Generalized Lorentz spaces and applications
• Convolution operator and maximal function for the Dunkl transform
• Ulteriori proprieta di alcune classi di funzioni in piu variabili
• Positive \(L^p\)-bounded Dunkl-type generalized translation operator and its applications
• Generalized heat equation and applications
• A proof of Trudinger's inequality and its application to nonlinear Schrödinger equations
• Differential-Difference Operators Associated to Reflection Groups
• Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability, and superweights for 𝐿^{𝑝}-weighted Hardy inequalities
• An Introduction to Dunkl Theory and Its Analytic Aspects
• Trudinger type inequalities in $\mathbf {R}^N$ and their best exponents
• Hardy-type inequalities for Dunkl operators with applications to many-particle Hardy inequalities
• New Progress on Weighted Trudinger–Moser and Gagliardo–Nirenberg, and Critical Hardy Inequalities on Stratified Groups
• Paley–Wiener theorems for the Dunkl transform

This page was built for publication: Rellich, Gagliardo-Nirenberg, Trudinger and Caffarelli-Kohn-Nirenberg inequalities for Dunkl operators and applications