Function spaces of Lorentz-Sobolev type: Atomic decompositions, characterizations in terms of wavelets, interpolation and multiplications
Blanca F. Besoy, Fernando Cobos
Abstract
We establish atomic decompositions and characterizations in terms of wavelets for Besov-Lorentz spaces BqsLp,r(Rn) and for Triebel-Lizorkin-Lorentz spaces FqsLp,r(Rn) in the whole range of parameters. As application we obtain new interpolation formulae between spaces of Lorentz-Sobolev type. We also remove the restrictions on the parameters in a result of Peetre on optimal embeddings of Besov spaces. Moreover, we derive results on diffeomorphisms, extension operators and multipliers for BqsLp,∞(Rn). Finally, we describe BqsLp,r(Rn) as an approximation space, which allows us to show new sufficient conditions on parameters for BqsLp,r(Rn) to be a multiplication algebra.
Topics & Concepts
MathematicsSobolev spaceLorentz transformationLorentz spaceInterpolation spaceWaveletInterpolation (computer graphics)Type (biology)Pure mathematicsBesov spaceFunction spaceMathematical analysisExtension (predicate logic)Functional analysisClassical mechanicsGeneProgramming languageAnimationPhysicsArtificial intelligenceBiologyComputer graphics (images)ChemistryBiochemistryEcologyComputer scienceAdvanced Harmonic Analysis ResearchMathematical Analysis and Transform MethodsAdvanced Mathematical Physics Problems