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 Mar 7 awarded Popular Question Nov 29 awarded Popular Question Jun 9 awarded Self-Learner May 27 awarded Notable Question Feb 15 awarded Notable Question Dec 13 awarded Popular Question Nov 16 awarded Notable Question Nov 16 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 $M$? Nov 16 asked Improvement of weak type inequality for Hardy-Littlewood Maximal inequality Oct 27 accepted Lebesgue space and weak Lebesgue space Oct 11 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. Oct 11 comment Lebesgue space and weak Lebesgue space In addition, Chebyshev's inequality should be used to prove $\|f\|_{wL^q} \le \|f\|_{L^q}$ Oct 11 comment Lebesgue space and weak Lebesgue space Don't you use the Holder inequality? Oct 11 comment Lebesgue space and weak Lebesgue space Is $p\le q$ also a necessary and sufficient condition for the inclusion? Oct 11 accepted Unique solution of system of differential equation Oct 11 accepted Norm of Hardy-Littlewood maximal operator Oct 9 accepted Application of weak $L^p$ estimate besides for proving boundedness of some linear operator Oct 9 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 $\mathbb{R}^n$. Oct 9 asked Norm of Hardy-Littlewood maximal operator Oct 9 revised Lebesgue space and weak Lebesgue space added 295 characters in body