2019/01/31 by Andrei Velicu
Mathematics · #Algebra over a field #Hardy space #Holomorphic and Operator Theory #Inequality #Kantorovich inequality #Ky Fan inequality #Mathematical Analysis and Transform Methods #Root (linguistics) #Spectral Theory in Mathematical Physics #Type (biology) #math.FA
paper · pdf · doi:10.1142/s0219199720500248
crossref issued 2020/06/15 · crossref published 2020/06/15 · crossref published-online 2020/06/15 · openalex publication_date 2020/06/15 · crossref created 2020/06/15 · arxiv created 2020/06/19 · arxiv updated 2020/06/22 · openalex created_date 2020/06/25 · crossref deposited 2021/07/23 · crossref published-print 2021/09/01 · crossref indexed 2026/08/03 · openalex updated_date 2026/08/05
In this paper, we study various forms of the Hardy inequality for Dunkl operators, including the classical inequality, [Formula: see text] inequalities, an improved Hardy inequality, as well as the Rellich inequality and a special case of the Caffarelli–Kohn–Nirenberg inequality. As a consequence, one-dimensional many-particle Hardy inequalities for generalized root systems are proved, which in the particular case of root systems [Formula: see text] improve some well-known results.