A second alternative approach for the study of the Muckenhoupt class $$A_1({\mathbb {R}})$$

Abstract

We find the exact best possible range of those $$p >1$$ for which any $$\varphi \in A_1({\mathbb {R}})$$ , with $$A_1$$ constant equal to c, must also belong to $$L^p$$ . In this way, we provide an alternative proof of the corresponding result in Bojarski and Sbordone (Studia Math 101(2):155–163, 1992) and Nikolidakis (Ann Acad Scient Fenn Math 40:949–955, 2015).