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seen Nov 16 at 2:21

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 $M$?
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
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 $\mathbb{R}^n$.
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?
Apr
17
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 $f(x,y)=x^3-y^3$?
Apr
12
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
Apr
12
comment Two variable function with four different stationary points
Thanks @Ian Coley
Apr
12
comment Two variable function with four different stationary points
Sorry, it is my typo
Mar
18
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 $q\geq 1$.
Mar
18
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?
May
17
comment Solving $x^{\log(x)}=\frac{x^3}{100}$
why prince Charles?
May
17
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 $0$
May
17
comment Two random variable with the same variance and mean
is the identity $E(XY|X)=XE(Y|X)$ easy to prove?
May
15
comment length of sum of two submodule
@rschwieb: But I only prove the cases $K \cap N =\{0\}$
May
15
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?
May
15
comment length of sum of two submodule
How to show that l((K+N)/N)=l(K+N)-l(N)?