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Mario C. Matos, Leopoldo Nachbin (1981)
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Mario C. Matos, Leopoldo Nachbin (1981)
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We prove that generalized Cantor sets of class α, α ≠ 2 have the extension property iff α < 2. Thus belonging of a compact set K to some finite class α cannot be a characterization for the existence of an extension operator. The result has some interconnection with potential theory.
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We establish an exponential estimate for the relationship between the ergodic maximal function and the maximal operator associated with convolution powers of a probability measure.
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