Let $T(f):=\frac{1}{x}\int_{0}^{x}{f(t)\,\mathrm{d}t}$ (the Hardy operator) find the norm of $T$ on $L^p$
49916
Computing the best constant in classical Hardy's inequality
38761
Is the $ L^{p}$$[0,1]$ norm continuous in p?
32092
Gelfand transformation of $l^p$
66953
How to prove Laplace transform is bounded on $L^2(\mathbb{R}_+)$?
60685
The vector space formed on C[0,1] and the norm $(\int_{0}^{1}|f(t)|^2 dt)^{1/2} $
106531
A Fourier transform of a continuous $L^1$ function
154612
$\int_{0}^{x} f(t) dt \ge {f(x)}$ holds or not on $[0,1]$
66084
Prove 1-Norm is a Norm
154913
Are all the norms of $L^p$ space equivalent?
109099
Prove that $\lim_{h \to 0}\frac{1}{h}\int_0^h{\cos{\frac{1}{t}}dt} = 0$
142025
How can I show that if $f\in L^p(a, b)$ then $\lim_{t\to 0^{+}}\int_{a}^b |f(x+t)-f(x)|^p\ dx=0$..
128457
Show that $T$ is a compact operator
149997
Convolution operator has norm 1 with respect to $L^2$ norm
46746
How to prove if $u\in W^{1,p}$, then $|u|\in W^{1,p}$?
87582
Some inequalities between 1- norm, 2- norm and infinity-norm: $\|x\|_2\leq\sqrt{\|x\|_1\| x\|_\infty}\leq\frac{1+\sqrt{n}}{2}\|x\|_2$
148759
The Radon-Nikodym derivative of a measure such that $|\int f'\,d\mu|\le \|f\|_{L^2}$ for $f\in C^1$
29114
If $f \in L^{p_1}(E) $ is bounded then $f\in L^{p_2}$ for any $p_2>p_1$