If $f^2$ and $f^3$ are $C^{\infty}(\mathbb R)$ then $f$ is $C^{\infty}(\mathbb R)$
118096
If $f^2$ and $f^3$ are smooth, does it follow that $f$ is smooth?
58597
A characterization of functions from $\mathbb R^n$ to $\mathbb R^m$ which are continuous
140437
If $a_0\in R$ is a unit, then  $\sum_{k=0}^{\infty}a_k x^k$ is a unit in $R[[x]]$
33081
If $\int_{\Bbb R^2}|f(x+iy)|\,dx\,dy<\infty$ then prove that $f\equiv 0$
80920
Prove or disprove: For any $v\in\mathbb{R}^n, \|v\|_1\|v\|_\infty \leq \frac{1+\sqrt{n}}{2}\|v\|_2^2$
138911
Is $\mathbb R^2$ a field?
81196
Is true that $H^{s,p}(\mathbb{R}^n)\subset C^k(\mathbb{R}^n)$ when $s-k>n/p$?.
150896
Show that $\lim_{p \to \infty} \| f \|_p = \| f \|_\infty$
14840
$c_0$ is a closed subspace of $l^{\infty}$
157455
Show that the norm of the multiplication operator $M_f$ on $L^2[0,1]$ is $\|f\|_\infty$
21269
Bijective continuous function between $(0 ,\infty)$ and $\mathbb{R}$.
25646
What is the result of $\infty - \infty$?
72644
Continuous injective map $f:\mathbb{R}^3 \to \mathbb{R}$?
13732
$||f||_p\to ||f||_\infty$ under general assumptions
57967
Difference between $\mathbb C$ and $\mathbb R^2$
129243
Is $C_{c}^{\infty}[a,b]$ a complete metric space?
111128
The Duals of $l^\infty$ and $L^{\infty}$