Open AccessImproved critical Hardy inequality and Leray-Trudinger type inequalities in Carnot groups
Author(s) -
Van Hoang Nguyen
Publication year - 2021
Publication title -
annales fennici mathematici
Language(s) - English
Resource type - Journals
eISSN - 2737-114X
pISSN - 2737-0690
DOI - 10.54330/afm.112567
Subject(s) - carnot cycle , inequality , mathematics , type (biology) , pure mathematics , mathematical analysis , thermodynamics , physics , geology , paleontology
In this paper, we prove an improvement of the critical Hardy inequality in Carnot groups. We show that this improvement is sharp and can not be improved. We apply this improved critical Hardy inequality together with the Moser-Trudinger inequality due to Balogh, Manfredi and Tyson (2003) to establish the Leray-Trudinger type inequalities which extend the inequalities of Psaradakis and Spector (2015) and Mallick and Tintarev (2018) to the setting of Carnot groups.