Properties of scales of Kato classes, Bessel potentials, Morrey spaces, and a weak Harnack inequality for non-negative solutions of elliptic equations

Abstract

In this article, we study some basic properties of the scale of Kato classes related with the Bessel kernel, Lorentz spaces, and Morrey spaces. Also we characterize the weak Harnack inequality for non-negative solutions of elliptic equations in terms of the Bessel kernel and the Kato classes of order $\alpha$.

Keywords

• Kato class
• Bessel potential
• Riesz potential
• Lorentz space
• weak Harnack inequality