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Title:Self improving Orlicz-Poincare inequalities
Author(s):DeJarnette, Noel
Director of Research:Tyson, Jeremy T.
Doctoral Committee Chair(s):Li, Xiaochun
Doctoral Committee Member(s):Tyson, Jeremy T.; Wu, Jang-Mei; Erdogan, M. Burak
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(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.
Issue Date:2014-01-16
URI:http://hdl.handle.net/2142/46744
Rights Information:Copyright 2013 Noel DeJarnette
Date Available in IDEALS:2014-01-16
Date Deposited:2013-12


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