Let be a homogeneous space, , a doubling measure on induced by a Haar measure on the group , a positive measure on and a weight on . Consider the maximal operator given by
In this paper, we obtain, for each , a necessary and sufficient condition for the boundedness of the maximal operator from to . As an application, we obtain a necessary and sufficient condition for the boundedness of the Poisson integral of functions defined on the unit sphere of the Euclidian space , from to , where is the Lebesgue measure on , is a weight on and is a positive measure on the unit ball of .
Cite this article
Iara A. A. Fernandes, Sergio A. Tozoni, Weighted Norm Inequality for a Maximal Operator on Homogeneous Space. Z. Anal. Anwend. 27 (2008), no. 1, pp. 67–78DOI 10.4171/ZAA/1344