GRA:020117The centered maximal function of 1_[0,1] has a three-unit quarter-level set, not a doubled-interval guessGra2 Centered Hardy Littlewood MaximalGra2 Weak Type Level Set MeasurePrivateLabels unavailablePrivate saving unavailableDifferentiation of measures and absolute continuityGraduate Real Analysis II · Mixed reviewProgress not loaded
GRA:020218A triangular hat transforms to sinc squared and Plancherel makes sinc fourth integrate to 2/3Gra2 Fourier Convolution TheoremGra2 Plancherel Sinc FourthPrivateLabels unavailablePrivate saving unavailableFourier transform and convolutionGraduate Real Analysis II · Mixed reviewProgress not loaded
GRA:020219Two integrable endpoint singularities convolve to a pi plateau before the arcsine tailGra2 Beta Function Singular KernelGra2 Truncated Convolution LimitsPrivateLabels unavailablePrivate saving unavailableFourier transform and convolutionGraduate Real Analysis II · Mixed reviewProgress not loaded
GRA:020220A boundary jump leaves a one-over-k Fourier tail even when the interior derivative is harmlessGra2 Integration BY Parts FourierGra2 Fourier Decay From JumpsPrivateLabels unavailablePrivate saving unavailableFourier transform and convolutionGraduate Real Analysis II · Mixed reviewProgress not loaded
GRA:020221The Hilbert transform of an interval indicator is logarithmic, odd, and still L2Gra2 Principal Value HilbertGra2 Hilbert L2 IsometryPrivateLabels unavailablePrivate saving unavailableFourier transform and convolutionGraduate Real Analysis II · Mixed reviewProgress not loaded
GRA:020322A symmetric box average rounds the absolute-value cusp by exactly epsilon over twoGraduate Real Analysis 2 Box Mollified CuspGraduate Real Analysis 2 Mollifier C1 Not C2PrivateLabels unavailablePrivate saving unavailableApproximate identities and densityGraduate Real Analysis II · Mixed reviewProgress not loaded
GRA:020325Compact truncation reaches an L2 tail at an exact rate while the same function never enters L1Graduate Real Analysis 2 L2 Tail TruncationGraduate Real Analysis 2 L2 Not L1 HalflinePrivateLabels unavailablePrivate saving unavailableApproximate identities and densityGraduate Real Analysis II · Mixed reviewProgress not loaded
GRA:020423Weak convergence does not commute with squaring: sqrt(2) sin(2 pi n x) vanishes while its energy tends to oneGraduate Real Analysis 2 Oscillatory Square Weak LimitGraduate Real Analysis 2 Weak Limit NonlinearPrivateLabels unavailablePrivate saving unavailableWeak convergence of functions and measuresGraduate Real Analysis II · Mixed reviewProgress not loaded
GRA:020426The powers x^n are weak-star null in L-infinity while their supremum norm never movesGraduate Real Analysis 2 X Power Weak StarGraduate Real Analysis 2 Weak Star Versus NormPrivateLabels unavailablePrivate saving unavailableWeak convergence of functions and measuresGraduate Real Analysis II · Mixed reviewProgress not loaded
GRA:020524The polynomial x(1-x) passes the sharp Dirichlet Poincare inequality with quotient one tenthGraduate Real Analysis 2 Dirichlet Poincare LedgerGraduate Real Analysis 2 Rayleigh Quotient PolynomialPrivateLabels unavailablePrivate saving unavailableDistributions and introductory Sobolev spacesGraduate Real Analysis II · Mixed reviewProgress not loaded
GRA:020527A translated delta derivative carries a testing minus sign, a Fourier multiplier, and a phaseView access optionsGra2 Translated Delta Testing PairingGra2 Tempered Fourier Multiplier PhasePrivateLabels unavailablePrivate saving unavailableDistributions and introductory Sobolev spacesGraduate Real Analysis II · Mixed reviewProgress not loaded
GRA:020528An interval indicator belongs to fractional H^s exactly below one half, with a computable Gagliardo blow-upView access optionsGra2 Gagliardo Seminorm IndicatorGra2 Fractional Sobolev ThresholdPrivateLabels unavailablePrivate saving unavailableDistributions and introductory Sobolev spacesGraduate Real Analysis II · Mixed reviewProgress not loaded
GRA:020529A lacunary Fourier tail has unit L2 mass and dies at the H one-half endpointView access optionsGra2 Lacunary Fourier SeriesGra2 Sobolev HS Threshold TorusPrivateLabels unavailablePrivate saving unavailableDistributions and introductory Sobolev spacesGraduate Real Analysis II · Mixed reviewProgress not loaded
GRA:020630Vanishing escaping mass converges weakly but stays exactly one unit away in Wasserstein oneView access optionsGra2 Weak Convergence Bounded ContinuousGra2 Wasserstein One GapPrivateLabels unavailablePrivate saving unavailableProbability measures, tightness, and convergence in lawGraduate Real Analysis II · Mixed reviewProgress not loaded
GRA:020631Right-endpoint empirical mass approximates the uniform law at exact Wasserstein rate one over two nView access optionsGra2 Empirical Quantile CouplingGra2 Wasserstein One RatePrivateLabels unavailablePrivate saving unavailableProbability measures, tightness, and convergence in lawGraduate Real Analysis II · Mixed reviewProgress not loaded