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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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Hilbert kernel regularity main part

Hilbert_kernel_regularity_main_part

Plain-language statement

For $0<y\le1$ and $y/2\le y'\le1$ , with both $y$ and $y'$ nonnegative, the negative-side Hilbert kernel satisfies the quantitative regularity estimate

$\lVert k(-y)-k(-y')\rVert \le 2^6\,\frac{1}{|y|}\,\frac{|y-y'|}{|y|}.$

harmonic analysisFourier analysismeasure theory

Source project: Carleson formalization

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