Next talk of the Seminar (17:00, Room Sousa Pinto)
26/11/2024: “On the solvability theory of singular integral
operators with nonCarleman shift”
Rui Marreiros (Universidade do
Algarve)
Next talk of the Seminar (16:00, Room Sousa Pinto)
29/11/2024: “MDM
property”
Michal Wojciechowski (Institute of Mathematics, Polish Academy of
Sciences, Warsaw, Poland)
Classical result of Mitiagin and Mirkhil 
DeLeeuw says that the uniform norm of a homogeneous partial derivative of a
function with compact support can be majorized by the norms of collections
of other homogeneous derivatives (of the same order) iff
its symbol is a linear combination of the symbols of the collection. The
simplest case
when it does not hold is a mixed
second derivative of function of two variables which can be unbounded while
second pure derivatives are bounded. In the talk I will show the analog of
this fact for analytic functions of two complex variables defined on the
bidisc. (the compact support condition is replaced here by boundedness of
all derivatives of smaller order). Our construction is based on
RudinShapiro polynomials.
It is a joint work with Krystian Kazaniecki.
This Seminar is supported in part by the
Portuguese Foundation for Science and Technology (FCT  Fundação para a Ciência e a Tecnologia),
through CIDMA  Center for Research and Development in Mathematics and
Applications, within project UIDB/04106/2020
(https://doi.org/10.54499/UIDB/04106/2020).
