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## Colloquium Mathematicum

### Tom 131 / 2013

Colloquium Mathematicum 131 (2013), 113-128 MSC: Primary 42B25; Secondary 46E40. DOI: 10.4064/cm131-1-10

#### Streszczenie

Properties of a maximal function for vector-valued martingales were studied by the author in an earlier paper. Restricting here to the dyadic setting, we prove the equivalence between (weighted) $L^p$ inequalities and weak type estimates, and discuss an extension to the case of locally finite Borel measures on $\mathbb {R}^n$. In addition, to compensate for the lack of an $L^\infty$ inequality, we derive a suitable $\rm {BMO}$ estimate. Different dyadic systems in different dimensions are also considered.

#### Autorzy

• Mikko KemppainenDepartment of Mathematics and Statistics
University of Helsinki
FI-00014 Helsinki, Finland
e-mail

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