Boundedness of both discrete Hardy and Hardy–Littlewood maximal operators via Muckenhoupt weights
Samir H. Saker, Ramy R. Mahmoud
Abstract
We employ the self-improving property (backward propagation) for the discrete Muckenhoupt class 𝒜p, to prove that both discrete Hardy and discrete Hardy–Littlewood maximal operators are bounded on the usual weighted Lebesgue space ℓup(ℤ+) if and only if the weight u belongs to 𝒜p. Some weak boundedness results for the Hardy–Littlewood maximal operators will also be discussed. To the best of the authors’ knowledge, the results are essentially new and have not been discussed before.
Topics & Concepts
MathematicsHardy spaceBounded functionStandard probability spacePure mathematicsClass (philosophy)Uniform boundednessLebesgue integrationProperty (philosophy)Space (punctuation)Lp spaceDiscrete mathematicsMathematical analysisBanach spacePhilosophyEpistemologyComputer scienceLinguisticsArtificial intelligenceAdvanced Harmonic Analysis ResearchHolomorphic and Operator TheoryAdvanced Banach Space Theory