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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 ...
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 ...
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, ...
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 ...
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 ...
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 ...
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 ...
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 ...