Abstract
In this note we give sufficient conditions on two dyadic systems on a space of homogeneous type in order to obtain the equivalence of corresponding Haar systems on Lebesgue spaces. The main tool is the vector-valued Fefferman–Stein inequality for the Hardy–Littlewood maximal operator.
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Communicated by Michael Lacey.
The authors were supported by UNL-CONICET-ANPCYT (Argentina).
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Aimar, H., Bernardis, A. & Nowak, L. Equivalence of Haar Bases Associated with Different Dyadic Systems. J Geom Anal 21, 288–304 (2011). https://doi.org/10.1007/s12220-010-9148-x
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DOI: https://doi.org/10.1007/s12220-010-9148-x