Abstract
<abstract><p>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.</p></abstract>
Highlights
We prove Hardy type inequalities for the fractional relativistic operator by using two different techniques
In order to get the latter, we study the solutions of the associated extension problem
Apart from the potential applications to partial differential equations, Hardy inequality is an interesting object of investigation and its study goes beyond the Euclidean setting or the Laplacian operator
Summary
Apart from the potential applications to partial differential equations, Hardy inequality is an interesting object of investigation and its study goes beyond the Euclidean setting or the Laplacian operator. This inequality plays an important role in many areas such as the spectral theory, geometric estimates and analyticity of functions. Sharp Hardy inequalities for the fractional relativistic operator may imply consequences on existence and nonexistence of solutions to problems involving Hs and different potentials. The Hardy inequality obtained in the second part is an improvement in the sense that the error in the inequality is explicitly computed, allowing the discussion on the sharpness
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
