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Self-Improving Properties of John–Nirenberg and Poincaré Inequalities on Spaces of Homogeneous Type

✍ Scribed by Bruno Franchi; Carlos Pérez; Richard L Wheeden

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
421 KB
Volume
153
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

✦ Synopsis

dedicated to professor bruno pini on his 80th birthday

We give a condition which ensures that if one inequality of Sobolev Poincare type is valid then other stronger inequalities of a similar type also hold, including weighted versions. Our main result includes many previously known results as special cases. We carry out the analysis in the context of spaces of homogeneous type, but the main result is new even in the usual Euclidean setting.

1998 Academic Press

1. Introduction

The purpose of this paper is to unify and generalize some results that have appeared recently concerning Poincare inequalities. We are interested in knowing when the existence of one inequality of this type implies that others also hold. This question has been studied recently by several authors, but the approach we will use is different, our key result being an article no. FU973175

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