{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/46744"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/46744","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Self improving Orlicz-Poincare inequalities","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.","abstract_html":"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.","abstract_has_math":false,"creators":["DeJarnette, Noel"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Tyson, Jeremy T.","Li, Xiaochun","Wu, Jang-Mei","Erdogan, M. 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