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ABC conjectureabstractabstract lang completenessactionadditive combinatoricsadele ringadic valuationaffine groupaffine spacesahiv22ahiv22supportalgebraic geometryalgorithmallow denyallows termalmost orthogonalityalmost periodicityanalysisanalytic number theoryanalytic setangular momentumangular velocityantichain operatorantichain tile countappendapprox hom pfrapproximationarcaritharithmetic geometryarithmetic progressionsas tensorasymptoticsasync runtimeauthorizationauthorizeauthorizerautomata theoryautomorphismauxiliaryball extensionball scalingbase changebase permbasicbasicsbasisbasis linearbatched evaluatorbehavioural theoryberlekamp welchbig opbijectivitybilinear formbindingbirthdaybisimulationbivariateblock rel distancebmobn254borel caratheodorybounding mutualbraketbridgebrownian motionbrun titchmarshbuchi congrbuchi congruencebuchi interbundledbundled semanticscaching logging oraclecaching oraclecadlagcadlag modificationcalculationscampanatocan reach 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Rcarleson general

rcarleson_general

Plain-language statement

Let $1<q\le2$ and let $q'$ be its Hölder conjugate. For measurable sets $F,G\subseteq\mathbb{R}$ and measurable $f$ with $\lVert f(x)\rVert\le\mathbf{1}_F(x)$ , the real-line Carleson operator satisfies

$\int_G^+ T f(x)\,dx \le C(q)\,\mu(G)^{1/q'}\mu(F)^{1/q}.$

harmonic analysisFourier analysismeasure theory

Source project: Carleson formalization

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