# Strobl18

Harmonic Analysis and Applications

June 4-8, 2018

Strobl, AUSTRIA

### "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}

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