Browsing Department of Mathematics (MU) by Thesis Advisor "Grafakos, Loukas"
Now showing items 1-10 of 10
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Almost everywhere convergence for modified Bochner Riesz means at the critical index for [rho] [greater than or equal to] 2
(University of Missouri--Columbia, 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 Schwarz-Christoffel transformation
(University of Missouri--Columbia, 2017)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Let [omega] be an open and connected set in the complex plane. A mapping f : [omega] [right arrow] C is said to be conformal at a point z0 if it ... -
Counting theorems and inverse function theorems for analytic functions
(University of Missouri--Columbia, 2017)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] In this master's thesis, we discuss the counting and Rouche's theorems. These theorems are used to find the roots of complex analytic functions.Also, ... -
Directional time-frequency analysis with applications
(University of Missouri--Columbia, 2006)The purpose of this dissertation is to introduce a new directionally-sensitive time frequency representation of a function. It is shown that we may break up a function (or signal) into individual time-frequency-direction ... -
Distributional estimates for multilinear operators
(University of Missouri--Columbia, 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 Missouri--Columbia, 2017)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] Let [omega] be an open and connected subset of the complex plane. A real valued function u : [omega] [right arrow] R is said to be harmonic if it has ... -
Linear and multilinear spherical maximal functions
(University of Missouri--Columbia, 2020)In dimensions n [greater than or equal to] 2 we obtain Lp1(Rn) x...x Lpm(Rn) to Lp(Rn) boundedness for the multilinear spherical maximal function in the largest possible open set of indices and we provide counterexamples ... -
Maximal Fourier integrals and multilinear multiplier operators
(University of Missouri--Columbia, 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 Littlewood-Paley theory and BMO
(University of Missouri--Columbia, 2012)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] In this thesis we discuss some important results in Littlewood-Paley theory and the space of Bounded-Mean Oscillation functions, henceforth called ... -
Weak hardy spaces and paraproducts /
(University of Missouri--Columbia, 2016)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT REQUEST OF AUTHOR.] 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 ...