247A, Notes 2: The Hardy–Littlewood maximal function and applications

— 1. The Hardy-Littlewood maximal inequality — We work in Euclidean space with Lebesgue measure; we write instead of for the Lebesgue measure of a set . For any and let denote the open ball of radius centred at . Thus for instance . For any , we use to denote the dilate of around […]