A weighted maximal inequality for differentially subordinate martingales
Authors:
Rodrigo Bañuelos and Adam Osękowski
Journal:
Proc. Amer. Math. Soc. 146 (2018), 2263-2275
MSC (2010):
Primary 60G44; Secondary 42B25
DOI:
https://doi.org/10.1090/proc/13912
Published electronically:
January 12, 2018
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: The paper contains the proof of a weighted Fefferman-Stein inequality in a probabilistic setting. Suppose that ,
are martingales such that
is differentially subordinate to
, and let
be a weight, i.e., a nonnegative, uniformly integrable martingale. Denoting by
,
the maximal functions of
and
, we prove the weighted inequality
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where

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Additional Information
Rodrigo Bañuelos
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Email:
banuelos@math.purdue.edu
Adam Osękowski
Affiliation:
Department of Mathematics, Informatics and Mechanics, University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
Email:
ados@mimuw.edu.pl
DOI:
https://doi.org/10.1090/proc/13912
Keywords:
Martingale,
differential subordination,
weight
Received by editor(s):
January 4, 2017
Received by editor(s) in revised form:
July 30, 2017
Published electronically:
January 12, 2018
Additional Notes:
The first author was supported in part by NSF Grant #0603701-DMS
The second author was supported in part by the NCN grant DEC-2014/14/E/ST1/00532.
Communicated by:
Svitlana Mayboroda
Article copyright:
© Copyright 2018
American Mathematical Society