Probabilistic Littlewood-Paley theory

Authors

Deniz Karli, University of Connecticut

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 R^d× R⁺ . We define the harmonic extension of an L^P &parl0;R^d&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. ^

Recommended Citation

Karli, Deniz, "Probabilistic Littlewood-Paley theory" (2010). Doctoral Dissertations. AAI3411469.
https://digitalcommons.lib.uconn.edu/dissertations/AAI3411469