# Simon Bortz

### Analysis Seminar – Bruno Poggi (University of Minnesota)

ZoomTitle. Additive and scalar-multiplicative Carleson perturbations of elliptic operators on domains with low dimensional boundaries. Abstract. At the beginning of the 90s, Fefferman, Kenig and Pipher (FKP) obtained a rather sharp (additive) perturbation result for the Dirichlet problem of divergence form elliptic operators. Without delving into details, the point is that if the (additive)

### Bingyang Hu (Purdue University)

ZoomTitle: On a structure theorem of doubling weights, Muckenhoupt Ap weights and reverse Holder weights. Abstract: In this talk, I will introduce a way to construct an explicit family of measures on the real line that are p-adic doubling for any finite set of primes, however, not doubling. This part generalizes the work of Boylan,

### Analysis Seminar – Fernando Lopez-Garcia (Cal State Poly – Pomona)

ZoomTitle: A local-to-global method for inequalities in weighted Sobolev spaces. Abstract: In this talk, we will discuss a certain local-to-global technique with applications to inequalities in weighted Sobolev spaces, such as fractional Poincaré-type inequalities and Korn and conformal Korn inequalities. This technique is based on a certain decomposition of functions that extends the validity of the inequalities

### 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 – 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