Some remarks on the dyadic Rademacher maximal function

• Autorzy: Mikko Kemppainen
• Języki publikacji: EN

Abstrakty

EN

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 ℝⁿ. In addition, to compensate for the lack of an $L^∞$ inequality, we derive a suitable BMO estimate. Different dyadic systems in different dimensions are also considered.

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 42B25: Maximal functions, Littlewood-Paley theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 131
• Numer: 1
• Strony: 113-128

Daty

wydano

2013

Twórcy

autor

Mikko Kemppainen

• Department of Mathematics and Statistics, University of Helsinki, FI-00014 Helsinki, Finland

Identyfikatory

DOI

10.4064/cm131-1-10