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I'm encountering some problems when reading Lions' paper "the concentration-compactness principle in the calculus of variations. The limit case, Part 2". The Hardy-Littlewood-Sobolev (HLS) ...

Let $f: X \to \mathbb{R}$ be an upper semi-continuous function on $X$, which is a compact subspace of a vector space. Let sequence $x_n, n \in \mathbb{N}$, with positive elements - periodic: there ...

I would like to summarize various sufficient conditions for various modes of convergence of Fourier series. The followings are what I have gathered so far: $L^p$ convergence: if $f \in L^p(\mathbb{T}...