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Boundedness of Maximal Functions on Nondoubling Parabolic Manifolds with Ends
Let M be a nondoubling parabolic manifold with ends. First, this paper investigates the boundedness of the maximal function associated with the heat semigroup MΔf(x):=supt>0|e−tΔf(x)| where Δ is the Laplace–Beltrami operator acting on M. Then, by combining the subordination formula with the previous result, we obtain the weak type (1,1) and Lp boundedness of the maximal function MkL√f(x):=supt>0|(tL−−√)ke−tL√f(x)| on Lp(M) for 1
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