Geodesic
Some remarks on the dyadic Rademacher maximal function
Mikko Kemppainen1
1 Department of Mathematics and Statistics University of Helsinki FI-00014 Helsinki, Finland
Colloquium Mathematicum, Tome 131 (2013) no. 1, pp. 113-128

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/cm131-1-10
Keywords: properties maximal function vector valued martingales studied author earlier paper restricting here dyadic setting prove equivalence between weighted inequalities weak type estimates discuss extension locally finite borel measures mathbb addition compensate lack infty inequality derive suitable bmo estimate different dyadic systems different dimensions considered

Mikko Kemppainen 1

1 Department of Mathematics and Statistics University of Helsinki FI-00014 Helsinki, Finland 
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Mikko Kemppainen. Some remarks on the
 dyadic Rademacher maximal function. Colloquium Mathematicum, Tome 131 (2013) no. 1, pp. 113-128. doi: 10.4064/cm131-1-10

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