Title

Probabilistic Littlewood-Paley theory

Date of Completion

January 2010

Keywords

Mathematics

Degree

Ph.D.

Abstract

In this dissertation, we study the solution to a Dirichlet problem on the upper-half space Rd× R+ . We define the harmonic extension of an LP &parl0;Rd&parr0; function with respect to a product process of a d-dimensional symmetric stable process and 1-dimensional Brownian motion. Using this harmonic extension, we introduce Littlewood-Paley functions and prove some results on norm comparability of a function f and its corresponding Littlewood-Paley function. As a result of the operators obtained, we prove a multiplier theorem. ^