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A1 Fefferman–Stein inequality for maximal functions of martingales in uniformly smooth spaces

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Let f be a martingale with values in a uniformly p-smooth Banach space and w any positive weight. We show that E(f∗ ·w) . E(Spf ·w∗), where ·∗ is the… Click to show full abstract

Let f be a martingale with values in a uniformly p-smooth Banach space and w any positive weight. We show that E(f∗ ·w) . E(Spf ·w∗), where ·∗ is the martingale maximal operator and Sp is the ` sum of martingale increments.

Keywords: maximal functions; functions martingales; inequality maximal; stein inequality; uniformly smooth; fefferman stein

Journal Title: Electronic Journal of Probability
Year Published: 2021

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