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

Carnot D. Kenfack¹ ; Benoît F. Sehba²

¹ Département de Mathématiques Faculté des Sciences Université de Yaoundé I B.P. 812 Yaoundé, Cameroun
² Department of Mathematics University of Ghana Legon, P.O. Box LG 62 Legon, Accra, Ghana

Colloquium Mathematicum, Tome 142 (2016) no. 2, pp. 211-226

Résumé

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 $1\le p,q\infty$.

Détail

DOI : 10.4064/cm142-2-4

Keywords: omega koll bonami weight complete characterization positive measures int mathcal omega biggl int mathcal omega bigg mathcal lambda frac lambda biggl int mathcal omega bigg where omega weighted hardy littlewood maximal function upper half plane nbsp mathcal infty