Can $\|f\|_p\to\infty$ arbitrarily slowly? (Looking for hints.)
10805
How slow/fast can $L^p$ norm grow?
135700
Show that $\lim_{n \to \infty} (1/n)\sum_{i=1}^n f(x_i)$ exists
63418
Show that $f_n(x) = \frac{x^2}{n}$ for $x \in \mathbb{R}$ does not converge uniformly towards $0$ for $n \rightarrow \infty$
99675
A closed ball in $l^{\infty}$ is not compact
122911
Characterization of weak convergence in $\ell_\infty$
119133
there is $M<\infty$ such that $\sum_{n} |\hat{f}(n)|\le M\int_{0}^{2\pi}|f(t)|dt$ for each $f\in X$
57014
Existence of a power series converging non-uniformly to a continuous function
150896
Show that $\lim_{p \to \infty} \| f \|_p = \| f \|_\infty$
149601
$\lim_{x\to{\infty}} (x-\sqrt{x^2+x})$
123981
Is it possible to write any bounded continuous function as a uniform limit of smooth functions
49604
Can a function "grow too fast" to be real analytic?
50472
If monotone decreasing and $\int_0^\infty f(x)dx <\infty$ then $\lim\limits_{x\to\infty} xf(x)=0.$
44706
Behavior of $\sum a_n x^n$ given $\sum |a_n - a_{n-1}| < \infty$
79011
If $(F:E)<\infty$, is it always true that $\operatorname{Aut}(F/E)\leq(F:E)?$
60520
Upper bound for $|f(0)|$ based on its behavior within the unit disk.
91523
Prove this limit as $x\to\infty$
8503
Limit of $L^p$ norm when $p\to0$