On generalized maximal functions

Schröder, Bernd S. W.

doi:10.1090/S0002-9939-1993-1158009-5

On generalized maximal functions
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by Bernd S. W. Schröder PDF

Proc. Amer. Math. Soc. 118 (1993), 619-625 Request permission

Abstract:

In this paper we study the question of under what circumstances the quantity $||{\sup _{t < \infty , a \in \mathbb {R}}}|\int _0^t f (a,{M_s}) d{M_s}|\;|{|_p}$ is comparable to $||M_\infty ^{\ast }|{|_p}$, where ${M_t}$ is a continuous martingale and $f$ is a bounded Borel-measurable function.

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On generalized maximal functions and distorted local times