Ergodic Theory and Dynamical Systems · 1996 · 53 citations · 14 references
Natural SciencesMathematicsDynamical SystemsProbability TheoryStochastic ProcessesEntropyErgodic TheoryLimit TheoremsErgodic PropertiesErgodicityPointwise Ergodic Theorems
Abstract Given the usual averages in ergodic theory, let n 1 ≤ n 2 ≤ … and . There is a strong inequality ‖ Sf ‖ 2 ≤ 25‖ f ‖ 2 and there is a weak inequality m { Sf > λ} ≤ (7000/λ)‖f‖ 1 . Related results and questions for other variants of this square function are also discussed.
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