**"The boundedness of the Cesaro means in variable dyadic martingale Hardy spaces"**
#### Szarvas, Kristóf\begin{document}
We consider three types of maximal operators and we will prove that (under some conditions) each maximal operator is bounded from the classical dyadic martingale Hardy space $H_{p}$ to the classical Lebesgue space $L_{p}$ and from the variable dyadic martingale Hardy space $H_{p(\cdot)}$ to the variable Lebesgue space $L_{p(\cdot)}$. Using this, we can prove the boundedness of the Cesaro- and Riesz maximal operator from $H_{p(\cdot)}$ to $L_{p(\cdot)}$ and from the variable Hardy-Lorentz space $H_{p(\cdot),q}$ to the variable Lorentz space $L_{p(\cdot),q}$. As a consequence, we can prove theorems about almost everywhere- and norm convergence.
\end{document} |