Is there a way to think about Fatous theorem in terms of approximate identity?
What puzzles me is that we are moving non-tangentially towards the boundary when we consider Fatous theorem while my intuition on approximate identities is that we have some spike isolating behaviour at a point and this happens on a circle. I must have missed something since I cant figure out how to view it in order to get something which is reasonable.
The theorems and theory Ive been reading is on harmonic functions with bounded pth means, i.e the "harmonic hardy spaces".
My question might also be completely wierd and have no meaning what so ever.