Inequalities for the differential subordinates of Martingales, harmonic functions and Ito processes

In Chapter 1 we sharpen Burkholder's inequality μ(\vert v\vert\geq1)\leq2\Vert u\Vert\sb1 for two harmonic functions u and v by adjoining an extra assumption. That is, we prove the weak-type inequality μ(\vert v\vert\geq1)\leq K\Vert u\Vert\sb1 under the assumptions that $\vert v(\xi)\vert\leq\vert u(\xi)\vert, \vert\nabla v\vert\leq\vert\nabla u\vert$ and the extra assumption that $\nabla u\cdot\nabla v$ = 0. Here μ is the harmonic measure with respect to $\xi$ and the constant 1 $<K<$ 2, found by Davis, is the best constant in Kolmogorov's weak-type inequality for conjugate functions.

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

2011

Author dc:creator

• Choi, Changsun

Contributors dc:contributor

• Ruan, Zhong-Jin

• Mathematics

Statement dc:rights

• Copyright 1995 Choi, Changsun

Language dc:language

eng

Identifier

AAI9624313
(UMI)AAI9624313

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/19178