Poincaré inequalities for the maximal function

2019 
We study generalized Poincare´ inequalities. We prove that if a function satisfies an inequality of Poincare´ type, then the Hardy-Littlewood maximal function also obeys an estimate of similar form. As a by-product, we get a unified approach to proving that the maximal operator is bounded on Sobolev, Lipschitz and BMO spaces.
    • Correction
    • Source
    • Cite
    • Save
    • Machine Reading By IdeaReader
    0
    References
    10
    Citations
    NaN
    KQI
    []