Operator valued BMO and commutators

If E is a Banach space, b ∈ BMO(Rn, L(E) and T is a L(E)-valued Calderón-Zygmund type operator with operator-valued kernel k, we show the boundedness of the commutator Tb(f) = bT(f) − T(bf) on Lp(Rn,E) for 1 < p < ∞ whenever b and k verify some commuting properties. Some endpoint estimates are also provided

The Weiss conjecture on admissibility of observation operators for contraction semigroups

We prove the conjecture of George Weiss for contraction semigroups on Hilbert spaces, giving a characterization of infinite-time admissible observation functionals for a contraction semigroup, namely that such a functional C is infinite-time admissible if and only if there is an M > 0 such that parallel to IC(sI - A)(-1)parallel to less than or equal to M/root Re s for all s in the open right half-plane. Here A denotes the infinitesimal generator of the semigroup. The result provides a simultaneous generalization of several celebrated results from the theory of Hardy spaces involving Carleson measures and Hankel operators

Transhumant GPS tracked sheep flocks from lowlands to highlands in Spain: grazing resources use and difficulties of walking/herding

The need for preserving walking/herding transhumance drove roads on the Iberian Peninsula hasbeen widely recognized, as they provide a wide range of ecosystem services. In spite of the decline of walkingtranshumance in Spain, some drove roads are being reactivated due mainly to the high price of lorrytransport and feeds for livestock. The objectives of this work were: (i) develop a method to track the transhumantflocks in order to know the route followed and detail the type of pastures that the sheep use during thetrip; (ii) know the main difficulties of the activity, either technical, economic or social. Collars with GPS wereinstalled around the neck of some animals of five transhumant flocks. The data provided by GPS were analyzedby a GIS and overlapped with pastures/vegetation maps. For each flock, interviews with the farmersprovided data in terms of difficulties for the activity to be continued. The method provided highly accurate dataof the routes. The main types of vegetation used by sheep and main difficulties perceived by the farmers tocontinue the activity are summarized