Open AccessHardy type inequalities for the fractional relativistic operator
Author(s) -
Luz Roncal,
Bilbao Euskal Herriko Unibertsitatea
Publication year - 2021
Publication title -
mathematics in engineering
Language(s) - English
Resource type - Journals
ISSN - 2640-3501
DOI - 10.3934/mine.2022018
Subject(s) - operator (biology) , inequality , type (biology) , mathematics , extension (predicate logic) , trace (psycholinguistics) , pure mathematics , order (exchange) , representation (politics) , algebra over a field , calculus (dental) , mathematical physics , mathematical analysis , computer science , philosophy , political science , linguistics , chemistry , economics , geology , law , biochemistry , transcription factor , programming language , finance , politics , gene , dentistry , paleontology , medicine , repressor
We prove Hardy type inequalities for the fractional relativistic operator by using two different techniques. The first approach goes through trace Hardy inequalities. In order to get the latter, we study the solutions of the associated extension problem. The second develops a non-local version of the ground state representation in the spirit of Frank, Lieb, and Seiringer.