In this work we characterize the pairs of weights (w, v) such that the one-sided Hardy-Littlewood maximal function in dimension two is of weak-type (p, p), 1 ≤ p ≤ ∞, with respect to the pair (w, v). As an application of ...

We characterize inverse limits of nilsystems in topological dynamics, via a structure theorem for topological dynamical systems that is an analog of the structure theorem for measure preserving systems. We provide two ...

will discuss the problem of optimizing (i.e., maximizing or minimizing) the upper Lyapunov exponent of a matrix cocycle. The main result to be presented, joint with Michal Rams (Warsaw), says that if a 2x2 one-step cocycle has ...

En 2005, B. Host y B. Kra [24] probaron la convergencia de algunos promedios ergódicos múltiples introduciendo para cada d \in N un factor que caracteriza el comportamiento de estos promedios. En 2010, B. Host, B. Kra y ...

We employ the ergodic-theoretic machinery of scenery flows to address classical geometric measure-theoretic problems on Euclidean spaces. Our main results include a sharp version of the conical density theorem, which we ...