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Maximal function and Carleson measures in the theory of Békollé–Bonami weights

Volume 142 / 2016

Carnot D. Kenfack, Benoît F. Sehba Colloquium Mathematicum 142 (2016), 211-226 MSC: Primary 42B25; Secondary 42A61. DOI: 10.4064/cm142-2-4

Abstract

Let $\omega$ be a Békollé–Bonami weight. We give a complete characterization of the positive measures $\mu$ such that $$ \int_{\mathcal H}|M_\omega f(z)|^q\,d\mu(z)\le C\biggl(\int_{\mathcal H}|f(z)|^p\omega(z)\,dV(z)\bigg)^{q/p} $$ and $$ \mu(\{z\in \mathcal H: Mf(z)>\lambda\})\le \frac{C}{\lambda^q}\biggl(\int_{\mathcal H}|f(z)|^p\omega(z)\,dV(z)\bigg)^{q/p}, $$ where $M_\omega$ is the weighted Hardy–Littlewood maximal function on the upper half-plane $\mathcal H$ and $1\le p,q<\infty$.

Authors

  • Carnot D. KenfackDépartement de Mathématiques
    Faculté des Sciences
    Université de Yaoundé I
    B.P. 812
    Yaoundé, Cameroun
    e-mail
  • Benoît F. SehbaDepartment of Mathematics
    University of Ghana
    Legon, P.O. Box LG 62
    Legon, Accra, Ghana
    e-mail

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