Self improving Orlicz-Poincare inequalities

Orlicz Functions;Poincare inequality;maximal function operator

DeJarnette, Noel

关键词: Orlicz Functions;    Poincare inequality;    maximal function operator;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/46744/Noel_DeJarnette.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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 giveexamples in the plane that show all hypotheses are required and developthe 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.