Browsing Department of Mathematics (MU) by Thesis Advisor "Grafakos, Loukas"
Now showing items 18 of 8

Almost everywhere convergence for modified Bochner Riesz means at the critical index for [rho] [greater than or equal to] 2
(University of MissouriColumbia, 2010)The Fourier transform is a mathematical operation that can be used with its inverse to rewrite a function as a sum of waves. It has been a useful mathematical tool for many applied sciences. Sometimes Fourier inversion is ... 
Conformal mappings and the SchwarzChristoffel transformation
(University of MissouriColumbia, 2017)Let ? be an open and connected set in the complex plane. A mapping f : ? ? C is said to be conformal at a point z0 if it preserves angles and orientation between curves intersecting at z0. We discuss tangent lines and their ... 
Directional timefrequency analysis with applications
(University of MissouriColumbia, 2006)The purpose of this dissertation is to introduce a new directionallysensitive time frequency representation of a function. It is shown that we may break up a function (or signal) into individual timefrequencydirection ... 
Distributional estimates for multilinear operators
(University of MissouriColumbia, 2005)We prove that if a multilinear operator and all its adjoints map L1 x x L1 to L1/m,oo, then the distribution function of the operator applied to characteristic functions of sets of finite measure has exponential decay at ... 
Harmonic functions and the Dirichlet problem
(University of MissouriColumbia, 2017)Let ? be an open and connected subset of the complex plane. A real valued function u : ? ? R is said to be harmonic if it has continuous first and second partial derivatives and satisfies Laplaces equation ?u = ? 2u ?x2 + ... 
Maximal Fourier integrals and multilinear multiplier operators
(University of MissouriColumbia, 2016)The first topic of this dissertation is concerned with the L^2 boundedness of a maximal Fourier integral operator which arises by transferring the spherical maximal operator on the sphere S^n to a Euclidean space of the ... 
Topics in LittlewoodPaley theory and BMO
(University of MissouriColumbia, 2012)In this thesis we discuss some important results in LittlewoodPaley theory and the space of BoundedMean Oscillation functions, henceforth called BMO. LittlewoodPaley Theory has its roots in the LittlewoodPaley Theorem, ... 
Weak Hardy spaces and paraproducts
(University of MissouriColumbia, 2016)The purpose of this dissertation is to provide a new square function characterization of weak Hardy spaces in the full range of exponents possible and use this characterization in applications on endpoint estimates for ...