4 papers · 1 filter
Differentiating along rectangles with fixed shapes in a set of directions
Emma D'Aniello, Laurent Moonens
In the present note, we examine the behavior of some homo\-thecy-invariant differentiation basis of rectangles in the plane satisfying the following requirement: for a given rectan…
On some generic small Cantor spaces
Emma D'Aniello, Martina Maiuriello
Let , . We show that the typical (in the sense of Baire category) compact subset of is not only a zero dimensional Cantor space but it satisfies the pro…
Differentiating Orlicz spaces with rare bases of rectangles
Emma D 'Aniello, Laurent Moonens, Joseph Rosenblatt
In the current paper, we study how the speed of convergence of a sequence of angles decreasing to zero influences the possibility of constructing a rare differentiation basis of re…
Averaging on -dimensional rectangles
Emma D'Aniello, Laurent Moonens
In this work we investigate families of translation invariant differentiation bases of rectangles in , for which is the largest Orlicz space that d…