Harmonic Analysis Seminar, Spring Semester '25-'26
Organizer: Georgios Sakellaris
Meeting Calendar
9/2/26: Introduction
Examples of Singular Integral Operators, the Hardy-Littlewood maximal function
(Presenter: Georgios Sakellaris)
26/2/26: Introduction (continued)
Approximations of the identity, Schwartz functions and tempered distributions, elements from Fourier Analysis
(Presenter: Georgios Sakellaris)
2/3/26: The Hilbert Transform
Basic properties, L^2 boundedness
(Presenter: Georgios Sakellaris)
9/3/26: The Hilbert transform (continued)
Poisson kernels, the Maximal Hilbert transform
(Presenter: Vasileios Marinos)
16/3/26: The Riesz transforms
L² boundedness, relations with the Laplacian
(Presenter: Alexandros Simichanidis)
23/3/26: Calderón-Zygmund theory
Calderón-Zygmund kernels, non convolution examples, the dyadic grid, the Calderón-Zygmund decomposition
(Presenter: Alexandros Simichanidis)
30/3/26: Calderón-Zygmund theory (continued)
The Calderón-Zygmund decomposition, the Calderón-Zygmund Theorem
(Presenter: Alexandros Simichanidis)
20/4/26: The Beurling Transform
(Presenter: Vasileios Marinos)
27/4/26: Truncations of Calderón-Zygmund Operators
Singular integral Calderón-Zygmund operators, and Cotlar's inequality
(Presenter: Alexandros Simichanidis)
4/5/26: The Hardy space H¹
Complex Hardy spaces, the real Hardy space H¹
(Presenter: Georgios Nikolaidis)
11/5/26: The Hardy space H¹ (continued)
Atoms, the atomic Hardy space, Calderón-Zygmund Operators on H¹
(Presenter: Georgios Nikolaidis)
18/5/26: The space BMO
Duality of H¹ and BMO, Calderón-Zygmund Operators and BMO
(Presenter: Georgios Sakellaris)