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Carleson's theorem is a fundamental result in mathematical analysis establishing the pointwise (Lebesgue) almost everywhere convergence of Fourier series of ''L''2 functions, proved by . The name is also often used to refer to the extension of the result by to ''L''''p'' 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. ==Statement of the theorem== The result, in the form of its extension by Hunt, can be formally stated as follows: : Let ''ƒ'' be an ''L''''p'' periodic function for some ''p'' ∈ (1, ∞), with Fourier coefficients . Then :: : for almost every ''x''. The analogous result for Fourier integrals can be formally stated as follows: : Let ''ƒ'' ∈ ''L''''p''(R) for some ''p'' ∈ (1, ∞) have Fourier transform . Then :: : for almost every ''x'' ∈ R. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Carleson's theorem」の詳細全文を読む スポンサード リンク
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