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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 \begin{equation} |\{x\in B : Mf(x)>\alpha\}| \ge \frac{2^{-d}}{\alpha}\int_{x\in B:|f(x)|>\alpha} |f(x)| \ dx ? \end{equation} 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
Oct
9
asked Lebesgue space and weak Lebesgue space
Sep
21
suggested rejected edit on How to simplify $(\sin\theta-\cos\theta)^2+(\sin\theta+\cos\theta)^2$?
Jul
2
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Jul
2
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May
25
comment Application of weak $L^p$ estimate besides for proving boundedness of some linear operator
Thank you for your reference.