arXiv subjects

Pedro Tradacete

Publications and source records attributed to Pedro Tradacete.

58 records · Page 4Linked to original sources

arXiv2014

Best constants for the Hardy-Littlewood maximal operator on finite graphs

We study the behavior of averages for functions defined on finite graphs $G$, in terms of the Hardy-Littlewood maximal operator $M_G$. We explore the relationship between the geometry of a graph and its maximal operator and prove that $M_G$ completely determines $G$ (even though embedding properties for the graphs do not imply pointwise inequalities for the maximal operators). Optimal bounds for the $p$-(quasi)norm of a general graph $G$ in the range $0<p\le1$ are given, and it is shown that the complete graph $K_n$ and the star graph $S_n$ are the extremal graphs attaining, respectively, the lower and upper estimates. Finally, we study weak-type estimates and some connections with the dilation and overlapping indices of a graph.

math.CO↗

arXiv2014

Banach lattice versions of strict singularity

We explore the relation between lattice versions of strict singularity for operators from a Banach lattice to a Banach space. In particular, we study when the class of disjointly strictly singular operators, those not invertible on the span of any disjoint sequence, coincides with that of lattice strictly singular operators, i.e. those not invertible on any (infinite dimensional) sublattice. New results are given which help to clarify the existing relation between these two classes.

math.FA↗

arXiv2013

Characterization of the restricted type spaces R(X)

We study functorial properties of the spaces $R(X)$, introduced in [Studia Math. 197 (2010), 69-79] as a central tool in the analysis of the Hardy operator minus the identity on decreasing functions. In particular, we provide conditions on a minimal Lorentz space $Λ_φ$ so that the equation $R(X)=Λ_φ$ has a solution within the category of rearrangement invariant (r.i.) spaces. Moreover, we show that if $R(X)=Λ_φ$, then we can always take $X$ to be the minimal r.i. Banach range space for the Hardy operator defined in $Λ_φ$.

math.FA↗

arXiv2013

Rearrangement invariant optimal range for Hardy type operators

We characterize, in the context of rearrangement invariant spaces, the optimal range space for a class of monotone operators related to the Hardy operator. The connection between optimal range and optimal domain for these operators is carefully analyzed.

math.FA↗