On the almost everywhere convergence of ergodic averages for power-bounded operators on LP-subspaces |
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| Authors: | Earl Berkson Jean Bourgain T. A. Gillespie |
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| Affiliation: | (1) Department of Mathematics, University of Illinois, 1409 W. Green Street, 61801 Urbana, Illinois, USA;(2) Etudes Scientifiques, Institut des Hautes, 35, Route de Chartres, 91440 Bures-sur-Yvette, France;(3) Department of Mathematics, University of Edinburgh, James Clerk Maxwell Building, EH9 3JZ Edinburgh, Scotland |
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| Abstract: | Let X be a closed subspace of LP( ), where is an arbitrary measure and 1. For an invertible power-bounded linear operator U: X X and n=1,2,..., letA(n) and  (n) denote the discrete ergodic averages and Hilbert transform truncates defined by U. We extend to this setting the -a. e. convergence criteria forA(n) and (n) which V. F. Gaposhkin and R. Jajte introduced for unitary operators on L2(). Our methods lift the setting from X to  p, where classical harmonic analysis and interpolation can be applied to suitable square functions. |
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