Some basic properties and fundamental relations for discrete Muckenhoupt and Gehring classes

Abstract

Abstract In this paper, we prove some basic properties of the discrete Muckenhoupt class A p $\mathcal{A}^{p}$ and the discrete Gehring class G q $\mathcal{G}^{q}$ . These properties involve the self-improving properties and the fundamental transitions and inclusions relations between the two classes.

Keywords

• Discrete Gehring’s class
• Discrete Muchenhoupt’s class
• Self-improving properties