Dissertation
A Modified Chang-Wilson-Wolff Inequality Via the Bellman Function
Doctor of Philosophy (PhD), Washington State University
01/2019
Handle:
https://hdl.handle.net/2376/16730
Abstract
We produce the optimal constant in an inequality bounding the exponential integral
of a function by the exponential integral of its dyadic square function. This work is
motivated by a well known result due to Chang, Wilson, and Wolff which controls the
exponential integral of a function in terms of the essential supremum of its dyadic square
function.
Perhaps more interesting than the result itself is the method of proof. We establish
our inequality and find the optimal constant using a Bellman function argument. This
type of argument was pioneered in the 1980s by Donald Burkholder in his work on
martingale transforms.
Along the way, we trace the origin of the Bellman function technique back to Richard
Bellman’s development of dynamic programming in the 1950s. Doing so provides some
historical context and lends insight into the genesis of Burkholder’s ideas.
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Details
- Title
- A Modified Chang-Wilson-Wolff Inequality Via the Bellman Function
- Creators
- Henry Riely
- Contributors
- Charles N Moore (Advisor)Kevin Vixie (Committee Member)Bala Krishnamoorthy (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Department of Mathematics and Statistics
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Number of pages
- 58
- Identifiers
- 99900581817101842
- Language
- English
- Resource Type
- Dissertation