Functional Analysis and Applications Seminar 

29/11/2002, 15:00 — 16:00 — Room P3.10, Mathematics Building
Stefan Samko, Universidade do Algarve, Faro

Periodization of Two-Dimensional Fractional Riesz Operators

We consider the periodization of the Riesz fractional integrals (Riesz potentials) of two variables and show that already in this case we come across different effects, depending on whether we use the repeated periodization, first in one variable, and afterwards in another one, or the so called double periodization. We show that the naturally introduced doubly-periodic Weyl-Riesz kernel of order less than 2, in general coincides with the periodization of the Riesz kernel, the repeated periodization being possible for all orders , while the double one is applicable only for orders less than 1. This is obtained as a realization of a certain general scheme of periodization, both repeated and double versions. We prove statements on coincidence of the corresponding periodic and non-periodic convolutions and give an application to the case of the Riesz kernel.