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Dec
14
comment control of an integral using maximal function
Great! Nice proof. We can also start with the case $I=[-0.5,0.5]$, which may be simpler.
Dec
14
accepted control of an integral using maximal function
Dec
14
comment control of an integral using maximal function
Also, I did not see the point in replacing $1+\frac{|x-c|}{\lambda(I)}$ by the max of the two summands. It seems that we can go with the sum.
Dec
14
comment control of an integral using maximal function
It seems to me that $(Mf_{a,b})(x)=(Mf)(a(x-b))$. So the (modified) last equality in your proof will give the desired result.
Dec
13
asked control of an integral using maximal function
Dec
13
accepted estimate of infinite norm by $(p,q)$ norms
Dec
10
comment estimate of infinite norm by $(p,q)$ norms
Great! So this is a true statement for f being a Schwartz function or a distribution, right?
Dec
10
comment estimate of infinite norm by $(p,q)$ norms
Sorry, but I still can't see why $f(x)^2=2\int_{-\infty}^xf'(t)f(t) dt$.
Dec
10
awarded  Informed
Dec
10
comment estimate of infinite norm by $(p,q)$ norms
Could you please give more details? I started with writing $f(x)=\int_{-\infty}^x f'(t) dt$, but did not know how to proceed. Also, if $f$ is the characteristic function of $[0,1]$, then it seems that the inequality is false.
Dec
9
awarded  Commentator
Dec
9
accepted an inequality on $L_p$ and $l_2$
Dec
9
comment an inequality on $L_p$ and $l_2$
I see. $l_p$ spaces are nested ($l_p$ gets larger when $p$ get bigger). Thank you!
Dec
6
asked an inequality on $L_p$ and $l_2$
Dec
6
comment sum over arbitrary subsets
I thought $\sum_{n\in \mathbb{Z}} a_n$ could be defined by the limit of $\sum_{n=-k}^{k} a_n$. For sum over $B$, we just consider the terms in the intersection of [-k,k] and B, then take limit.
Dec
6
comment estimate of infinite norm by $(p,q)$ norms
You are right. It is false when f' is very small. Is there any way to add an additional condition to make the statement true?
Dec
6
asked sum over arbitrary subsets
Dec
6
accepted control of an integral using the integral of derivative
Dec
6
asked estimate of infinite norm by $(p,q)$ norms
Dec
6
asked control of an integral using the integral of derivative