Analysis Seminar
Analysis Seminar – Alejandro Vélez-Santiago (University of Puerto Rico)
ZoomTitle: The Robin problem over irregular domains Abstract: We will discuss the solvability and global regularity theory for the Laplace equation with Robin boundary conditions over classes of irregular domains which include non-Lipschitz domains and domains with fractal boundaries.
Analysis Seminar – Olli Saari (University of Bonn)
ZoomTitle: On the weak differentiability of the fractional maximal function Abstract: The fractional maximal functions are comparable in Lp size to the Riesz potentials of same order. Its smoothing properties are however more subtle. In this talk, I will discuss Sobolev regularity of fractional maximal functions on the Euclidean n-space as well as on bounded
Analysis Seminar – Christos Grigoriadis (Michigan State University)
ZoomTitle: Necessary and sufficient conditions in weighted theory Abstract: Starting with the L^p boundedness of the Hilbert transform by Riesz in 1928 we go through the development of weighted theory. First Muckenhoupt and the necessary and sufficient A_p condition for one weight inequalities, then Sawyer with the testing conditions on two weight inequalities leading up
Analysis Seminar – Timothy Robertson (University of Tennessee)
ZoomTitle: Masuda's Uniqueness Theorem for Leray-Hopf Weak Solutions of Navier-Stokes Equations: Revisited Abstract: In this talk, we revisit the classical Masuda's theorem on the uniqueness of Leray-Hopf weak solutions for the system of Naiver-Stokes equations. We extend this uniqueness result to a class of Leray-Hopf weak solutions in mixed-norm Lebesgue spaces. The talk is based on my
Analysis Seminar – Simon Bortz (University of Alabama)
ZoomSimon Bortz is going to talk about the ideas in a recent paper which can be found at https://arxiv.org/abs/2008.11544. Roughly speaking, the talk will be about how a quantitative approximation scheme, in fact, gives a form of quantitative coincidence. The main theorem has some nice applications (e.g. transference of boundedness of singular integrals and `geometric
Analysis Seminar – Naga Manasa Vempati (Washington University, Saint Louis)
Title: The two-weight inequality for Calder\'on-Zygmund operators with applications and results on two weight commutators of maximal functions on spaces of homogeneous type. Abstract: For (X,d,w) be a space of homogeneous type in the sense of Coifman and Weiss, i.e. d is a quasi metric on X and w is a positive measure satisfying the doubling
Analysis Seminar – Alyssa Genschaw (University of Connecticut)
ZoomTitle: Solvability of the Dirichlet Problem with L^p Data for Caloric Measure Abstract: This talk concerns two probability measures. First, we consider harmonic measure, which gives solutions to the Dirichlet problem associated to Laplace's equation. Additionally, we may view harmonic measure as the “hitting probability" for Brownian motion. This probabilistic interpretation shows the connection between
Analysis Seminar – Trang Nguyen (University of South Australia)
ZoomTitle: Non-homogeneous T(1) theorem for singular integrals on product quasimetric spaces Abstract: In the Calderón-Zygmund Theory of Singular Integrals, the T(1) theorem of David and Journé is one of the most celebrated theorems. It gives easily-checked criteria for a singular integral operator T to be bounded from L^2(R^n) to L^2(R^n), meaning T(f) is bounded for
Analysis Seminar – Brandon Sweeting (University of Cincinnati)
ZoomTitle: Novel Bellman Estimates for Ap Weights Abstract: The Bellman function method is an assortment of tools for obtaining sharp inequalities in harmonic analysis. To handle an inequality, one fixes a set of parameters, called Bellman variables, and maximizes (or minimizes) the left-hand side subject to these constraints. The solution of the corresponding extremal problem
Analysis Seminar – Tuoc Phan (University of Tennesse, Knoxville)
ZoomTitle: Some recent results on L_p-theory for equations with singular and degenerate coefficients Abstract: We consider classes of elliptic and parabolic equations whose coefficients are singular or degenerate of the porotype $x_d^\alpha$ on the domain $\{x_d >0\}, where $\alpha$ is a real number. Two boundary conditions on \{x_d =0\}$ are studied: the homogeneous Diritchlet boundary