Lower bounds for the centered Hardy-Littlewood maximal operator on the real line

F. J. Pérez Lázaro

Let $1<p<\infty$. We prove that there exists an ${\epsilon }_p>0$ such that for each $f\in L^p(\mathbb{R})$, the centered Hardy-Littlewood maximal operator $M$ on $\mathbb{R}$ sati…