For questions inequalities which involves integrals, like Cauchy-Bunyakovsky-Schwarz or Hölder's inequality. To be used with (inequality) tag.
2
votes
1answer
94 views
Hilbert's Inequality
Could you help me to show the following:
The operator
$$
T(f)(x) = \int _0^\infty \frac{f(y)}{x+y}dy
$$
satisfies
$$\Vert T(f)\Vert_p \leq C_p \Vert f\Vert_p
$$
for $1 <p< \infty$ where
...
5
votes
1answer
378 views
Hölder inequality from Jensen inequality
I'm taking a course in Analysis in which the following exercise was given.
Exercise Let $(\Omega, \mathcal{F}, \mu)$ be a probability space. Let $f\ge 0$ be a measurable function.
Using Jensen's ...
