Is Fourier series also defined firstly as $L^1([a,b])→l^∞$, and can be extended to $L^p([a,b])→l^q$ where $p∈(1,2],1/p+1/q=1$ in some way similar to Fourier transform?
I didn't find the answer in the Wikipedia article for Fourier series, or some books I have. So references are also appreciated.
What can we say about generalized Fourier series?
Thanks and regards!