Carleson's theorem

Carleson's theorem is a fundamental result in <a href="/facts/Mathematical_analysis/XXeR26Ih">mathematical analysis</a> establishing the <a href="/facts/Pointwise/dt4Mrs6w">pointwise</a> (<a href="/facts/Lebesgue_measure/8us9cGoW">Lebesgue</a>) <a href="/facts/Almost_everywhere_convergence/TXGpeyIK">almost everywhere convergence</a> of <a href="/facts/Fourier_series/s3fsxPAT">Fourier series</a> of <a href="/facts/Lp_space/gbad0Rv1">L2 functions</a>, proved by <a href="/facts/Lennart_Carleson/drIokpo0">Lennart Carleson</a> (1966). The name is also often used to refer to the extension of the result by <a href="/facts/Richard_Hunt_(mathematician)/oRd3NLQw">Richard Hunt</a> (1968) to Lp functions for p ∈ (1, ∞] (also known as the Carleson–Hunt theorem) and the analogous results for pointwise almost everywhere convergence of <a href="/facts/Fourier_integral/XXhKJtc8">Fourier integrals</a>, which can be shown to be equivalent by transference methods.

Carleson's theorem open-in-new

Carleson's theorem