Director of Research (if dissertation) or Advisor (if thesis)
Tyson, Jeremy T.
Doctoral Committee Chair(s)
Li, Xiaochun
Committee Member(s)
Tyson, Jeremy T.
Wu, Jang-Mei
Erdogan, M. Burak
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Orlicz Functions
Poincare inequality
maximal function operator
Abstract
In [20], Keith and Zhong prove that spaces admitting Poincar e inequalities also admit a priori stronger Poincar e inequalities. We use their technique, with slight adjustments, to obtain a similar result in the case of Orlicz-Poincar e inequalities. We give examples in the plane that show all hypotheses are required and develop
the theory of Orlicz-Poincar e inequalities for nondoubling Young functions to show that the ∞-Poincar e inequality does not improve to any Orlicz-Poincar e inequality.
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