Let $X$,$Y$ be dependent random variables, $\mu_x$ and $\mu_y$ their expectation values and let $a_1$ and $a_2$ be natural numbers. Then I need a bound for the following formula:
$$ \mathbb{E} [(X-\mu_x)^{a_1} * (Y - \mu_y)^{a_2} ] \leq ??? $$
I dont have any informations about the distributions so a direct calculation is not possible.