Morrey–Campanato space

In mathematics, the Morrey–Campanato spaces (named after Charles B. Morrey, Jr. and Sergio Campanato)are Banach spaces which extend the notion of functions of bounded mean oscillation, describing situations where the oscillation of the function in a ball is proportional to some power of the radius other than the dimension.They are used in the theory of elliptic partial differential equations, since for certain values ofare Hölder continuous functions over the domainThe seminorm of the Morrey spaces is given by When, the Morrey space is the same as the usual, the spatial dimension, the Morrey space is equivalent to, due to the Lebesgue differentiation theorem.are equivalent to the Campanato spaces with the same value ofis a sufficiently regular domain, that is to say, when there is a constant A such that, the Campanato space is the space of functions of bounded mean oscillation., the Campanato space is the space of Hölder continuous functions, the space contains only constant functions.This mathematical analysis–related article is a stub.
mathematicsCharles B. Morrey, Jr.Sergio CampanatoBanach spacesbounded mean oscillationradiuselliptic partial differential equationsHölder continuousseminormLebesgue differentiation theoremPrinceton University PressFunctional analysistopicsglossaryBanachFréchetHilbertHölderNuclearOrliczSchwartzSobolevTopological vectorBarrelledCompleteLocally convexReflexiveSeparableHahn–BanachRiesz representationClosed graphUniform boundedness principleKrein–MilmanMin–maxGelfand–NaimarkBanach–AlaogluAdjointBoundedCompactHilbert–SchmidtNormalTrace classTransposeUnboundedUnitaryBanach algebraC*-algebraSpectrum of a C*-algebraOperator algebraGroup algebra of a locally compact groupVon Neumann algebraInvariant subspace problemMahler's conjectureHardy spaceSpectral theory of ordinary differential equationsHeat kernelIndex theoremCalculus of variationsFunctional calculusIntegral linear operatorJones polynomialTopological quantum field theoryNoncommutative geometryRiemann hypothesisDistributionGeneralized functionsApproximation propertyBalanced setChoquet theoryWeak topologyBanach–Mazur distanceTomita–Takesaki theorymathematical analysis