Self improving Orlicz-Poincare inequalities

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2014

Author dc:creator

• DeJarnette, Noel

Contributors dc:contributor

• Tyson, Jeremy T.
• Li, Xiaochun
• Wu, Jang-Mei
• Erdogan, M. Burak

• Orlicz Functions
• Poincare inequality
• maximal function operator

Statement dc:rights

• Copyright 2013 Noel DeJarnette

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/46744

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/46744