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VARIATIONAL INEQUALITIES FOR BILINEAR AVERAGES
Author(s) -
Liu Honghai,
Wang Hanbin
Publication year - 2020
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/mtk.12034
Subject(s) - mathematics , ergodic theory , bilinear interpolation , variational inequality , convergence (economics) , class (philosophy) , inequality , variable (mathematics) , mathematical analysis , pure mathematics , statistics , artificial intelligence , computer science , economics , economic growth
We establish variational inequalities for a class of bilinear averages of one variable, generalizing the variational inequalities for linear averages of Jones et al . As an application we obtain almost everywhere convergence for ergodic averages along cubes on a dynamical system.