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Zeitschrift für Analysis und ihre Anwendungen


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Volume 27, Issue 1, 2008, pp. 67–78
DOI: 10.4171/ZAA/1344

Published online: 2008-03-31

Weighted Norm Inequality for a Maximal Operator on Homogeneous Space

Iara A. A. Fernandes[1] and Ximena Mujica[2]

(1) Universidade São Francisco, Itatiba, Brazil
(2) Universidade Federal do Paraná, Curitiba, Brazil

Let $X=G/H$ be a homogeneous space, $\wid X=X\times [0,\infty)$, $\mu$ a doubling measure on $X$ induced by a Haar measure on the group $G$, $\beta$ a positive measure on~$\wid X$ and $W$ a weight on $X$. Consider the maximal operator given by \[ {\cal M} f(x,r)=\sup _{s\geq r} \frac{1}{\mu (B(x,s))}\int_{B(x,s)} |f(y)|\,d\mu (y), \quad (x,r)\in\wid X. \] In this paper, we obtain, for each $p, q, 1

Keywords: Maximal function, Poisson integral, homogeneous space, Ap-weights, sphere

Fernandes Iara, Mujica Ximena: Weighted Norm Inequality for a Maximal Operator on Homogeneous Space. Z. Anal. Anwend. 27 (2008), 67-78. doi: 10.4171/ZAA/1344