Functional Analysis, Linear Structures and Applications Seminar

Next session

Combinatorial Game Theory: a survey

In the first years of the 20th century the analysis of the game of NIM (by the mathematician Charles L. Bouton) triggered the outburst of a completely new mathematical subject: Combinatorial Game Theory. The aim of this seminar is to give a survey of the development of this mathematical field.

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.

Current organizers: Helena Mascarenhas, Ângela Mestre.