I am studying a graduate level course in Fourier Analysis, however my Functional Analysis background is extremely weak, I have also never met Lebesgue Integration and it has been a while since I covered any topology.
I would like the recommendation of a workbook or online course with Fourier Analysis questions at a basic level with solutions, or questions at a more advanced level with thorough solutions.
I'd like something like Kreyszig Functional Analysis but for Fourier, or some online exercises if such a thing is available.
Let me give a list:
"Fourier analysis" by T.W. Körner
Tolstov's little book on Fourier Analysis
Gerald Folland's book (see here)
Dym & McKean, "Fourier Series and Integrals"
E Gonzalez-Velasco, "Fourier Analysis and Boundary Value Problems"
Stein and Shakarchi, "Fourier Analysis: an introduction."