$\|f*g\|_q\leq \|g\|_q \|f\|_1$ and $\|f*g\|_\infty\leq \|g\|_q \|f\|_{q^{'}}$, $(1/q+1/q^{'}=1)$?
123005
$L^p$ Spaces, Young's Theorem, Convolutions, and Minkowski's Inequality
89429
Prove $\sup \left| f'\left( x\right) \right| ^{2}\leqslant 4\sup \left| f\left( x\right) \right| \sup \left| f''\left( x\right) \right| $
63124
Show that $ \lVert A \rVert_2^2 \leq \lVert A \rVert _1 \lVert A \rVert _ \infty $
82371
$f$ is an entire function with Im $f\geq 0$
19804
How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
45370
Is it true that $|d(x, z) - d(y, z)| \leq d(x, y)$ and how do I prove it?
142360
How to show $x_1,x_2, \dots ,x_n \geq 0 $ and $ x_1 + x_2 + \dots + x_n \leq \frac{1}{2} \implies (1-x_1)(1-x_2) \cdots (1-x_n) \geq \frac{1}{2}$
155974
Show $||Tx||_2 \leq ||(v_n)||_2 \cdot ||x||_{\infty}$
93806
$\|f\|_{L^{p}}=\sup\left\{\int_{{\bf R}^{n}}|f(x)g(x)|~dx:\|g\|_{L^{q}}\le1\right\}$
139674
Prove $\ln\frac{p}{q}\leq \frac{p-q}{\sqrt{pq}}$ for $0<q\leq p$
58562
How can we prove that $D(f)\backsimeq\operatorname{Spec} A_f$?
148981
Entire $f$ and $g$ constant if $e^{f(z)}+e^{g(z)}=1$
120985
Prove that $\mathrm{Res}[f/g,z_0]=\frac{f(z_0)}{g'(z_0)}$
130537
Proving that $d(f,g)=\|f-g\| = \sup \limits_{0\leq x \leq 1} |f(x)-g(x)|$ is a metric on $X=C[0,1]$
13270
Prove $\exists \xi \in (a,b):f'(\xi)<1+f^2(\xi)$
73696
Given $(a_n)$ with $a_n \geq a_{n+1} \geq 0$ show that if $\sum \sqrt{a_n a_{n+1}} < \infty \implies \sum a_n < \infty$
72470
Prove that $2|ab| \leq a^2 + b^2$ and $|a|+|b| \leq \sqrt {2}(a^2+b^2)^{1/2}$