On Friday, 31/05/2019, 17:00 — 18:00, in Room P3.10 of Mathematics Building of the IST will take place a seminar by Natasha Samko (UiT The Arctic University of Norway) with title
“On a class of Integral operators in central generalized Morrey spaces”.
We find conditions for the boundedness of integral operators $K$ which commute with dilations and rotations, in a central generalized Morrey space. We also show that under the same conditions these operators preserve the subspace of Morrey spaces, known as vanishing Morrey space. In the case of non-negative kernels, we also give necessary conditions for the boundedness. In the case of classical Morrey spaces the obtained sufficient and necessary conditions coincide with each other. In the one-dimensional case we also obtain similar results for global Morrey spaces. In the case of radial kernels we obtain stronger estimates of $Kf$ via spherical means of $f$. We demonstrate the efficiency of the obtained conditions for a variety of examples such as weighted Hardy operators, weighted Hilbert operator, their multi-dimensional versions and others.