0
$\begingroup$

a part of my task is to show that you can express

$\int\limits_{S_{1/2}(1/2 e_1)} \dfrac{1}{\vert x-z \vert ^n} \ dH(z)$

as

$\int\limits_{S_{1/2}(1/2 e_1)} \dfrac{1}{\vert x \vert ^n \vert z \vert ^n \vert \vert z^{*}-x^{*} \vert^n} \ dH(z)$

where $x \in B_{1/2}(1/2 e_1)$ and $x^{*}= \dfrac{x}{\vert x \vert ^2}$.

I tried different approaches but didn't success, for example I've tried to transform the integral into an integral over the 1-sphere but I still dont know how to solve the problem. Does anyone have any advices for me?

$\endgroup$

Your Answer

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

Browse other questions tagged or ask your own question.