This question was part of my assignment which couldn't be discussed due to pendamic.
If f $\in H(0<|z|<R)$ and $\int_{0<x^2+y^2<R} {|f(x+iy)|}^2 dx dy <\infty$ prove that f has either a removable singularity or a pole of order 1 at 0.
I have studied my class notes thoroughly but I am clueless on which result should I use in this problem.
function f is Holomorphic on disc 0<|z|<R . Removable singularity is a singular point of a function for which it is possible to assign a complex number in such a way that becomes analytic while pole of order 1 means that z f(z) is analytic as z approaches 0.
Can anyone please tell how should I approach this question ?
Thanks!!