Some remarks on the dyadic Rademacher maximal function

Mikko Kemppainen

Colloquium Mathematicae, Tome 131 (2013), p. 113-128 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $L^{\infty}$ inequality, we derive a suitable BMO estimate. Different dyadic systems in different dimensions are also considered.

Publié le : 2013-01-01

Zbl 1281.42020

EUDML-ID : urn:eudml:doc:283966

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     title = {Some remarks on the dyadic Rademacher maximal function},
     journal = {Colloquium Mathematicae},
     volume = {131},
     year = {2013},
     pages = {113-128},
     zbl = {1281.42020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-1-10}
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Mikko Kemppainen. Some remarks on the dyadic Rademacher maximal function. Colloquium Mathematicae, Tome 131 (2013) pp. 113-128. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-1-10/