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seen Oct 13 at 22:25

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 suggested edit on How to simplify $(\sin\theta-\cos\theta)^2+(\sin\theta+\cos\theta)^2$?
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
May
25
comment Application of weak $L^p$ estimate besides for proving boundedness of some linear operator
Thank you for your reference.
May
24
comment Application of weak $L^p$ estimate besides for proving boundedness of some linear operator
May I get the references for your argument (especially about Hardy-Littlewood Maximal operator)? In addition, can the density be applied for fractional integral operator?
May
23
asked Relation between fractional integral operator and solution of poisson equation
May
23
asked Application of weak $L^p$ estimate besides for proving boundedness of some linear operator
May
21
accepted existence of the solution of Neumann problem in $\mathbb{R}^3$
May
11
asked existence of the solution of Neumann problem in $\mathbb{R}^3$