We host talks in the fields of Analysis, as well as Applied Analysis. Please email uraltsev "at" uark "dot" edu if you would like to give a talk.
Abstract: The Cauchy-Riemann problem, also known as the $\overline\partial$-problem, is a central problem in several complex variables. It concerns the regularity estimates to the equation $\overline\partial u=f$ on forms in a bounded domain $\Omega\subset\mathbb C^n$. We will talk about some background of the $\overline\partial$-regularity theory, and the obstructions on solving the $\overline\partial$ equation when f is a generic distributions, and our recent works using new technique from extension operators. We use the so-called Rychkov's extension operator, which extends functions on a bounded Lipschitz domain and has boundedness on all Besov spaces and Triebel-Lizorkin spaces. This is based on multiple works which are in part joint with Ziming Shi and Yuan Zhang.
Location and Zoom link: SCEN 322 and at https://uark.zoom.us/j/87503165233?pwd=S7QdLHdFaJYEkZL3at0OV4aE2rRPwh.1
Abstract: TBA
Location and Zoom link: SCEN 322 and at https://uark.zoom.us/j/87503165233?pwd=S7QdLHdFaJYEkZL3at0OV4aE2rRPwh.1
Abstract: TBA
Location and Zoom link: SCEN 322 and at https://uark.zoom.us/j/87503165233?pwd=S7QdLHdFaJYEkZL3at0OV4aE2rRPwh.1
Abstract: TBA
Location and Zoom link: SCEN 322 and at https://uark.zoom.us/j/87503165233?pwd=S7QdLHdFaJYEkZL3at0OV4aE2rRPwh.1
Abstract: TBA
Location and Zoom link: SCEN 322 and at https://uark.zoom.us/j/87503165233?pwd=S7QdLHdFaJYEkZL3at0OV4aE2rRPwh.1