2
$\begingroup$

I was reading a paper and I found stated without proof or reference the following inequality:

$$\left(\sum_{i=1}^{m}\prod_{j=1}^{n}(\beta_{i}^j)^p\right)^{\frac{1}{p}}\leq \prod_{j=1}^{n}\left(\sum_{i=1}^{m}\left(\beta_{i}^{j}\right)^{p_j}\right)^{\frac{1}{p_j}}$$

where $\beta_i^j\geq 0$ and $\frac{1}{p_1}+\cdots\frac{1}{p_n}=\frac{1}{p}$

Anyone knows where I can find a proof for this?

Thanks in advance.

$\endgroup$
3
$\begingroup$

Use the generalized Hölder inequality with counting measure.

$\endgroup$
  • $\begingroup$ Thanks a lot for the answer, Milind! $\endgroup$ – Mark_Hoffman Dec 2 '15 at 9:12

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.