About: Carleson's theorem

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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 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.

Attributes	Values
rdf:type	Thing yago:WikicatTheoremsInAnalysis yago:Abstraction100002137 yago:Communication100033020 yago:Message106598915 yago:Proposition106750804 yago:Statement106722453 yago:Theorem106752293
rdfs:label	Satz von Carleson und Hunt (de) Carleson's theorem (en) Teorema de Carleson (es) Théorème de Carleson (fr) 칼레손의 정리 (ko)
rdfs:comment	In der Mathematik ist der Satz von Carleson und Hunt ein Lehrsatz über die punktweise Konvergenz von Fourier-Reihen. Er ist die Verallgemeinerung des vormals als Vermutung von Lusin bekannten Satzes von Carleson und ist nach Lennart Carleson und Richard Allen Hunt benannt. (de) 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. (en) Le théorème de Carleson est un résultat fondamental de l'analyse mathématique établissant la convergence ponctuelle presque partout de la série de Fourier des fonctions L2, c'est-à-dire de carré intégrable. Il a été prouvé par Lennart Carleson en 1966. Ce nom est également souvent utilisé pour se référer à l'extension du résultat proposée par Richard Hunt en 1968, aux fonctions Lp pour p ∈ ]1, +∞[ (connu sous le nom de Théorème de Carleson–Hunt) et aux résultats analogues de convergence ponctuelle presque partout des intégrales de Fourier, ce qui peut être démontré comme étant équivalent. (fr) El Teorema de Carleson es un resultado fundamental en análisis matemático para establecer (según la medida de Lebesgue) la convergencia en casi cualquier punto de las series de Fourier, por funciones L2. El nombre se utiliza a menudo para referirse a la extensión del resultado a las funciones de Lp de p ∈ (1, ∞) (también conocido como el teorema de Carleson-Hunt) y los resultados análogos para la convergencia en casi cualquier punto de las integrales de Fourier, que se puede demostrar de forma equivalente por métodos de transferencia. (es) 칼레손의 정리(영어: Carleson's theorem)는 L² 함수의 푸리에 급수가 거의 모든 곳에서 원래 함수로 수렴한다는 중요한 정리이다. 스웨덴 수학자 렌나르트 칼레손이 1966년에 증명하였다. 1968년에 미국 수학자 리처드 헌트는 이를 확장하여 p ∈ (1, ∞)일 때 Lp 함수에 대해서도 마찬가지임을 보였다. 때문에 이 결과를 칼레손-헌트 정리(영어: Carleson-Hunt theorem)라고도 부른다. 푸리에 변환에 대해서도 비슷한 결과가 성립한다. (ko)
differentFrom	Carlson's theorem
dct:subject	Theorems in Fourier analysis
Wikipage page ID	24105681 (xsd:integer)
Wikipage revision ID	1097931161 (xsd:integer)
Link from a Wikipage to another Wikipage	Cambridge University Press Bounded variation Annals of Mathematics Mathematical analysis Notices of the American Mathematical Society G. H. Hardy Bounded operator Convergence of Fourier series Lp space Fejér's theorem Acta Mathematica Cesàro summation Lebesgue measure Fourier coefficient Fourier series Fourier transform Theorems in Fourier analysis Pointwise convergence Paul du Bois-Reymond Pointwise Société Mathématique de France Maximal operator Periodic function Springer-Verlag Fourier integral Almost every Almost everywhere convergence Uniform boundedness theorem
Link from a Wikipage to an external page	http://www.mrlonline.org/mrl/2000-007-004/2000-007-004-001.html https://www.ams.org/notices/200702/comm-carleson.pdf http://matwbn.icm.edu.pl/tresc.php%3Fwyd=2&tom=26 http://www.essex.ac.uk/maths/people/fremlin/mt.htm https://eudml.org/doc/213617 https://web.archive.org/web/20080705224659/http:/www.mrlonline.org/mrl/2000-007-004/2000-007-004-001.html https://web.archive.org/web/20101101220236/http:/www.essex.ac.uk/maths/people/fremlin/mt.htm%23 http://www.numdam.org/item%3Fid=SB_1964-1966__9__491_0
sameAs	Carleson's theorem Carleson's theorem Carleson's theorem Carleson's theorem Carleson's theorem Carleson's theorem Carleson's theorem Carleson's theorem
dbp:wikiPageUsesTemplate	dbt:Open-closed dbt:Block_indent dbt:Citation dbt:Cite_book dbt:Distinguish dbt:Harv dbt:Harvtxt dbt:Math dbt:Mvar dbt:Short_description dbt:Abs dbt:Harvs dbt:Eom
authorlink	Richard Hunt (en) Charles Fefferman (en) Lennart Carleson (en) Nikolai Nikolaevich Luzin (en)
em	1.500000 (xsd:double)
first	Charles (en) Michael (en) Richard (en) Christoph (en) S.A. (en) Lennart (en) N. N. (en)
last	Hunt (en) Lacey (en) Thiele (en) Carleson (en) Fefferman (en) Luzin (en) Telyakovskii (en)
text	Let be an periodic function for some , with Fourier coefficients . Then for almost every . (en) Let for some have Fourier transform . Then for almost every . (en)

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