Besov space

In mathematics, the Besov space (named after Oleg Vladimirovich Besov)These spaces, as well as the similarly defined Triebel–Lizorkin spaces, serve to generalize more elementary function spaces such as Sobolev spaces and are effective at measuring regularity properties of functions.Several equivalent definitions exist.This definition is quite limited because it does not extend to the range s ≤ 0.Let and define the modulus of continuity by Let n be a non-negative integer and define: s = n + α with 0 < α ≤ 1.contains all functions f such that The Besov spaceis equipped with the norm The Besov spacescoincide with the more classical Sobolev spacesThis mathematical analysis–related article is a stub.

mathematicsOleg Vladimirovich BesovcompletequasinormedBanach spaceTriebel–Lizorkin spacesfunction spacesSobolev spacesmodulus of continuityGraduate Studies in MathematicsFunctional analysistopicsglossaryBanachFréchetHilbertHölderNuclearOrliczSchwartzSobolevTopological vectorBarrelledLocally 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