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 Feb15 awarded Notable Question Dec13 awarded Popular Question Nov16 awarded Notable Question Nov16 comment Improvement of weak type inequality for Hardy-Littlewood Maximal inequality Could you give the hint to prove this result or the reference? Is it related to weak type-(1,1) and strong type-$(\infty,\infty)$ for $M$? Nov16 asked Improvement of weak type inequality for Hardy-Littlewood Maximal inequality Oct27 accepted Lebesgue space and weak Lebesgue space Oct11 comment Lebesgue space and weak Lebesgue space Ah, I get it. However, I think that the Chebyshev inequality in the last inequality should be reversed. Oct11 comment Lebesgue space and weak Lebesgue space In addition, Chebyshev's inequality should be used to prove $\|f\|_{wL^q} \le \|f\|_{L^q}$ Oct11 comment Lebesgue space and weak Lebesgue space Don't you use the Holder inequality? Oct11 comment Lebesgue space and weak Lebesgue space Is $p\le q$ also a necessary and sufficient condition for the inclusion? Oct11 accepted Unique solution of system of differential equation Oct11 accepted Norm of Hardy-Littlewood maximal operator Oct9 accepted Application of weak $L^p$ estimate besides for proving boundedness of some linear operator Oct9 comment Norm of Hardy-Littlewood maximal operator Aguirre. Thank you very much. I have another question: Since the proof in Stein's book depend on the decomposition of $\mathbb{R}^n$, could we estend the inequality to $$|\{x\in B : Mf(x)>\alpha\}| \ge \frac{2^{-d}}{\alpha}\int_{x\in B:|f(x)|>\alpha} |f(x)| \ dx ?$$ Here, $B$ denotes the ball on $\mathbb{R}^n$. Oct9 asked Norm of Hardy-Littlewood maximal operator Oct9 revised Lebesgue space and weak Lebesgue space added 295 characters in body Oct9 asked Lebesgue space and weak Lebesgue space Sep21 suggested rejected edit on How to simplify $(\sin\theta-\cos\theta)^2+(\sin\theta+\cos\theta)^2$? Jul2 awarded Curious Jul2 awarded Inquisitive