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Boundedness of maximal functions on non-doubling manifolds with ends
Let be a manifold with ends constructed in \cite{GS} and be the
Laplace-Beltrami operator on . In this note, we show the weak type
and boundedness of the Hardy-Littlewood maximal function and of the
maximal function associated with the heat semigroup \M_\Delta f(x)=\sup_{t> 0}
|\exp (-t\Delta)f(x)| on for . The significance of
these results comes from the fact that does not satisfies the doubling
condition
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