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Dyadic weights on $\mathbb {R}^n$ and reverse Hölder inequalities

Tom 234 / 2016

Eleftherios N. Nikolidakis, Antonios D. Melas Studia Mathematica 234 (2016), 281-290 MSC: Primary 42B25. DOI: 10.4064/sm8621-6-2016 Opublikowany online: 5 August 2016

Streszczenie

We prove that for any weight $\phi $ defined on $[0,1]^n$ that satisfies a reverse Hölder inequality with exponent $p \gt 1$ and constant $c\ge 1$ on all dyadic subcubes of $[0,1]^n$, its non-increasing rearrangement $\phi ^\ast $ satisfies a reverse Hölder inequality with the same exponent and constant not more than $2^nc-2^n+1$ on all subintervals of the form $[0,t]$, $0 \lt t\le 1$. As a consequence, there is an interval $[p,p_0(p,c))=I_{p,c}$ such that $\phi \in L^q$ for any $q\in I_{p,c}$.

Autorzy

  • Eleftherios N. NikolidakisDepartment of Mathematics
    National and Kapodistrian University of Athens
    Zografou, GR-15784, Athens, Greece
    e-mail
  • Antonios D. MelasDepartment of Mathematics
    National and Kapodistrian University of Athens
    Zografou, GR-15784, Athens, Greece
    e-mail

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