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 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 $M$? 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? 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 $\mathbb{R}^n$. May25 comment Application of weak $L^p$ estimate besides for proving boundedness of some linear operator Thank you for your reference. May24 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? Apr17 comment Two variable function with four different stationary points effective diet pill, Thank you for your example. I hope that I can find simpler example. I think that we can ask, what happen the stationary point if $D=0$ just like $(0,0)$ is the saddle point of $f(x,y)=x^3-y^3$? Apr12 comment Determine the number of zeros in the first quadrant Just using the quadratic formula and $z=\frac{1}{2}-\sqrt{3}i$ is on the second quadrant Apr12 comment Two variable function with four different stationary points Thanks @Ian Coley Apr12 comment Two variable function with four different stationary points Sorry, it is my typo Mar18 comment A function $f:\mathbb{R} \to \mathbb{R}$ with infinite norm but finite weak seminorm @127.0.9.6. Well, after checking again, we have to restrict $q\geq 1$. Mar18 comment A function $f:\mathbb{R} \to \mathbb{R}$ with infinite norm but finite weak seminorm I really thank you for your help. Could you give the references related to this subject? If it is possible, how do I contact you? This problem related to my thesis. I have added the Dirac delta function that I mentioned as my example. May I modify your example and add it if you give your permission? If I do so, how do I give your credit as personal communication? May17 comment Solving $x^{\log(x)}=\frac{x^3}{100}$ why prince Charles? May17 comment Limit of $\lim_{x \to 0}\left (x\cdot \sin\left(\dfrac{1}{x}\right)\right)$ is $0$ or $1$? Your mistake: $\lim_{x\rightarrow 0} \frac{sin(1/x)}{1/x}\neq 1$ but $0$ May17 comment Two random variable with the same variance and mean is the identity $E(XY|X)=XE(Y|X)$ easy to prove? May15 comment length of sum of two submodule @rschwieb: But I only prove the cases $K \cap N =\{0\}$ May15 comment length of sum of two submodule thanks BenjaLim, i will try work on it. But could we prove this without exact sequence concept, instead of directly from definition of composition series? May15 comment length of sum of two submodule How to show that l((K+N)/N)=l(K+N)-l(N)?