@article{8bc8bf79888f48c7aeb7d3dc33364b18,
title = "On Dimension-Free Variational Inequalities for Averaging Operators in Rd ",
abstract = "We study dimension-free Lp inequalities for r-variations of the Hardy–Littlewood averaging operators defined over symmetric convex bodies in Rd.",
author = "Jean Bourgain and Mariusz Mirek and Stein, {Elias M.} and B{\l}a{\.z}ej Wr{\'o}bel",
note = "Funding Information: Jean Bourgain was partially supported by NSF Grant DMS-1301619. Mariusz Mirek was partially supported by the Schmidt Fellowship and the IAS Found for Math. and by the National Science Center, NCN Grant DEC-2015/19/B/ST1/01149. Elias M. Stein was partially supported by NSF Grant DMS-1265524. B la{\.z}ej Wr{\'o}bel was partially supported by the National Science Centre, NCN Grant 2014/ 15/D/ST1/00405. Publisher Copyright: {\textcopyright} 2018, Springer International Publishing AG, part of Springer Nature.",
year = "2018",
month = feb,
day = "1",
doi = "10.1007/s00039-018-0433-3",
language = "English (US)",
volume = "28",
pages = "58--99",
journal = "Geometric and Functional Analysis",
issn = "1016-443X",
publisher = "Birkhauser Verlag Basel",
number = "1",
}