Theorems in Fourier analysis

Carleson's theorem

Carleson's theorem is a fundamental result in mathematical analysis establishing the pointwise (Lebesgue) almost everywhere convergence of Fourier series of L2 functions, proved by Lennart Carleson. The name is also often used to refer to the extension of the result by Richard Hunt to Lp functions for p ∈ (1, ∞] (also known as the Carleson–Hunt theorem) and the analogous results for pointwise almost everywhere convergence of Fourier integrals, which can be shown to be equivalent by transference methods. (Wikipedia).

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Related pages

Pointwise | Lebesgue measure | Fejér's theorem | Bounded operator | Bounded variation | Fourier transform | Fourier series | Lp space | G. H. Hardy | Pointwise convergence | Periodic function | Convergence of Fourier series | Cesàro summation | Mathematical analysis