Variable Exponent Lebesgue Spaces and Hardy-Littlewood Maximal Function on p-Adic Numbers
L. F. Chacón-Cortés, Humberto Rafeiro
Abstract
In this paper we introduce variable exponent Lebesgue spaces where the underlying space is the field of the p-adic numbers. We prove many properties of the spaces and also study the boundedness of the maximal operator as well as its application to convolution operators.
Topics & Concepts
MathematicsStandard probability spaceLp spaceLebesgue's number lemmaPure mathematicsConvolution (computer science)ExponentLebesgue integrationSpace (punctuation)Function (biology)Maximal operatorField (mathematics)Variable (mathematics)Maximal functionOperator (biology)Mathematical analysisDiscrete mathematicsOperator theoryBounded functionBanach spaceRiemann integralFourier integral operatorTranscription factorRepressorEvolutionary biologyGenePhilosophyComputer scienceBiochemistryArtificial neural networkChemistryMachine learningLinguisticsBiologyadvanced mathematical theoriesAdvanced Harmonic Analysis ResearchAlgebraic Geometry and Number Theory