A note on the boundedness of solutions for fractional relativistic Schrödinger equations

Abstract

In this paper, we obtain the boundedness of solutions for a class of fractional elliptic equations driven by the relativistic Schrödinger operator [Formula: see text], with [Formula: see text]. The proof relies on a distributional Kato’s inequality for [Formula: see text] and on some properties of the Bessel kernel.

Keywords

• Fractional Schrödinger operators
• Kato’s inequality
• regularity results
• exponential decay