Extrapolation and interpolation of quasi-linear operators on martingales

From MaRDI portal
Publication:2548127

DOI10.1007/BF02394573zbMath0223.60021WikidataQ104759959 ScholiaQ104759959MaRDI QIDQ2548127

Donald L. Burkholder, Richard F. Gundy

Publication date: 1970

Published in: Acta Mathematica (Search for Journal in Brave)




Related Items

Martingale Orlicz-Hardy spacesMixed Norm Martingale Hardy Spaces and Applications in Fourier AnalysisNon-isomorphic complemented subspaces of the reflexive Orlicz function spaces $L^{\Phi }[0,1$] ⋮ Transformation formulae for continuous semimartingales and certain non-regular real functions on the sequence spaceipBMO: Oscillations, Self-Improvement, Gagliardo Coordinate Spaces, and Reverse Hardy InequalitiesDimension free bounds for the Hardy–Littlewood maximal operator associated to convex setsOn Maximal Inequalities for Purely Discontinuous Martingales in Infinite DimensionsA probabilistic approach to Hilbert transforms on free group von Neumann algebrasMartingale transforms between martingale Hardy-Amalgam spacesWeighted norm inequalities for maximal operator of Fourier seriesWeighted local estimates for singular integral operatorsCharacterizations of bounded mean oscillationSome recent developments in Fourier analysis and 𝐻^{𝑝}-theory on product domainsJohn-Nirenberg space on LCA groupsGeneralized grand Lorentz martingale spacesExistence and transportation inequalities for fractional stochastic differential equationsThe Kolmogorov Inequality for the Maximum of the Sum of Random Variables and Its Martingale AnaloguesStochastic Processes in the Decades after 1950Doob's maximal inequality and Burkholder-Davis-Gundy's inequality on Musielak-Orlicz spacesFROM BOUNDARY CROSSING OF NON-RANDOM FUNCTIONS TO BOUNDARY CROSSING OF STOCHASTIC PROCESSESMartingale inequalities on Musielak–Orlicz Hardy spacesMaximal inequalities and some applicationsH p -spaces of martingales, 0<p?1Brownian Motion with Partial InformationDoob’s and Burkholder-Davis-Gundy inequalities with variable exponentAn Extremal Property of Independent Random VariablesSquare functions and the Hamming cube: dualitySharp Square-Function Inequalities for Conditionally Symmetric MartingalesExit times of N-dimensional random walksThe best constant in the Davis inequality for the expectation of the martingale square functionMartingale Transforms with Unbounded MultipliersBurkholder’s inequalities in noncommutative Lorentz spacesAn interpolation of operators in the martingale $H_p$-spacesReinforced random walkMartingale inequalities in noncommutative symmetric spacesThe development of square functions in the work of A. ZygmundExtrapolation with weights, rearrangement-invariant function spaces, modular inequalities and applications to singular integralsAn extrapolation theorem on martingale spaces with A p weightsLes inegalites de sous-martingales, comme consequences de la relation de dominationOn the maximal inequalities of Burkholder, Davis and GundyUnconditional convergence of Fourier expansions in systems of product bases in Orlicz spacesProblems in harmonic analysis related to curvatureSharp maximal inequalities for the martingale square bracketMartingale inequalities on Hardy-Lorentz-Karamata spacesJohnson–Schechtman and Khintchine inequalities in noncommutative probability theoryBounded Mean Oscillation and Regulated MartingalesIntermittency and Chaos for a Nonlinear Stochastic Wave Equation in Dimension 1Some results concerning L\(^p(\mu)\)-spacesExponential self-improvement of generalized Poincaré inequalities associated with approximations of the identity and semigroupsSelf-improving properties for abstract Poincaré type inequalitiesNoncommutative Davis type decompositions and applicationsSome inequalities for \(p\)-variations of martingales.Real interpolation with a function parameter for martingale Hardy-Lorentz and BMO spacesA counterexample concerning the relation between decoupling constants and UMD-constantsExtensions of the John–Nirenberg theorem and applicationsCharacterization of uniform PL-convexity of complex Banach space by functions with two variablesMaximal inequalities for the Ornstein-Uhlenbeck processObstacle Problems Generated by the Estimates of Square FunctionA generalized Marcinkiewicz interpolation theorem and its applicationsA weighted norm inequality for Fourier seriesSome dichotomy results for functionals of Harris recurrent Markov chainsCommutators on dyadic martingalesPoisson equation, moment inequalities and quick convergence for Markov random walks.Extrapolation from \(A_{\infty}\) weights and applicationsRosenthal type inequalities for free chaosThe Green formula and \(H^ p\) spaces on treesInterpolation between continuous parameter martingale spaces: The real methodFinite element approximations of a class of nonlinear stochastic wave equations with multiplicative noiseMoments of randomly stopped sums -- revisitedOn inequalities for two-parameter martingalesOn an approach to boundary crossing by stochastic processesQuadratic variation functionals and dilation equationsThe continuity of the quadratic variation of two-parameter martingalesJohnson-Schechtman inequalities for noncommutative martingalesA new class of unbalanced Haar wavelets that form an unconditional basis for \(L_ p\) on general measure spacesOn the chaotic character of the stochastic heat equation. IIOperator-valued martingale transforms in rearrangement invariant spaces and applicationsStochastic integrals and BDG's inequalities in Orlicz-type spacesBurkholder's inequalities associated with Orlicz functions in rearrangement invariant spacesGrand martingale Hardy spaces for \(0<p \leq 1\)Martingale BMO spaces with continuous timeUpper bounds for the \(L_ p\)-norms of martingalesOn the chaotic character of the stochastic heat equation, before the onset of intermitttencyThe boundedness of the two-parameter Sunouchi operators on Hardy spacesSelf-improving properties of John-Nirenberg and Poincaré inequalities on spaces of homogeneous typeWeighted norm inequalities, off-diagonal estimates and elliptic operators. I: General operator theory and weightsExponential decay estimates for singular integral operatorsOn some inequalities for Doob decompositions in Banach function spacesNew martingale inequalities and applications to Fourier analysisThe foundational inequalities of D. L. Burkholder and some of their ramificationsWeak nonmild solutions to some SPDEsWeak type inequalities for conditionally symmetric martingalesA maximal inequality for fractional Brownian motionsNoncommutative Burkholder/Rosenthal inequalities\(L_{p,q }\)-norm estimates associated with Burkholder's inequalitiesChanges of law, martingales and the conditioned square functionWeighted norm inequality for operator on martingalesRosenthal type inequalities for martingales in symmetric spacesWeak norm inequalities for martingales and geometry of Banach spacesOn the existence and position of the farthest peaks of a family of stochastic heat and wave equationsSome new \(\Phi \)-moment martingale inequalities associated with concave functionsNoncommutative Burkholder/Rosenthal inequalities associated with convex functionsAtomic decompositions of martingale Hardy-Morrey spacesAspects of probabilistic Littlewood-Paley theorySelf-improvement of Poincaré type inequalities associated with approximations of the identity and semigroupsMartingale transforms and their projection operators on manifoldsMartingale Morrey-Campanato spaces and fractional integralsInitial measures for the stochastic heat equationThe sharp constant for the Burkholder-Davis-Gundy inequality and non-smooth pastingRosenthal inequalities in noncommutative symmetric spacesOn Wald's equation for \(U\)-statistical sumsInvestigation of Haar and Franklin series in Hardy spacesWeak type estimates associated to Burkholder's martingale inequalityInterpolation and \(\Phi \)-moment inequalities of noncommutative martingalesSome existence results for systems of impulsive stochastic differential equationsSharp maximal inequalities for stochastic processesBMO and \(H^{1}\) for the Ornstein-Uhlenbeck operatorRemarks on a theorem of Burkholder and GundyMartingale Musielak-Orlicz-Lorentz Hardy spaces with applications to dyadic Fourier analysis\(L^p\) self-improvement of generalized Poincaré inequalities in spaces of homogeneous typeMixed atomic decomposition of martingale weak Hardy-Morrey spacesInequalities for tails of adapted processes with an application to Wald's lemmaOne-sided maximal functions and H\(^p\)The Burgess Davis inequalities via Fefferman's inequalityÉquation de la chaleur associée à une fonction plurisousharmonique d'exhaustion et comportement frontièreOn Haar series of \(A\)-integrable functionsInterpolation methods for stochastic processes spacesOn an inequality of H. P. RosenthalAnalysis of a stratified Kraichnan flowMixed martingale Hardy spacesOn \(L^p\)-norm convergence of series with respect to product systemsAn inequality for the conditioned square functions on martingalesA martingale that occurs in harmonic analysisExit times of Brownian motion, harmonic majorization, and Hardy spacesStochastic integral representation of some martingalesNoncommutative Burkholder/Rosenthal inequalities. II: ApplicationsOn the martingale decompositions of Gundy, Meyer, and Yoeurp in infinite dimensionsHoeffding decomposition in \(H^1\) spacesMartingale Hardy spaces for \(0<p\leq 1\)Semi-discrete semi-linear parabolic SPDEsSquare functions for noncommutative differentially subordinate martingalesWalsh-Fourier series and their generalizations in Orlicz spacesPiecewise monotonic doubling measuresInequalities and duality results with respect to two-parameter strong martingalesConformal martingalesBoundedness of Cesàro and Riesz means in variable dyadic Hardy spacesWeighted norm inequalities for rough singular integral operatorsEta invariants and the hypoelliptic LaplacianSpatial ergodicity for SPDEs via Poincaré-type inequalitiesSemi-martingale inequalities via the Garsia-Rodemich-Rumsey lemma, and applications to local timesInterpolation between \(H^ p \)spaces: The complex methodThe Haar system as an unconditional basis in L\(_p[0,1\)] ⋮ Operator-valued martingale transformsWeighted estimates of singular integrals and their applicationsDomination inequality for martingale transforms of a Rademacher sequenceThe dialectics archetypes/types (universal categorical constructions/concrete models) in the work of Alexander GrothendieckPathwise versions of the Burkholder-Davis-Gundy inequalityPower and exponential moments of the number of visits and related quantities for perturbed random walks\(\Phi\)-moment martingale inequalities on Lorentz spaces with variable exponentsTwo-parameter martingale Orlicz-Hardy spaces



Cites Work