Potential operators, maximal functions, and generalizations of A∞

We derive weighted norm estimates which relate integral operators of potential type (fractional integrals) to corresponding maximal operators (fractional maximal operators). We also derive norm estimates for the maximal operators. The conditions that we impose on the weights involve A∞ conditions of “content type” which are weaker than the usual A∞ condition. The analysis is carried out in the context of spaces of homogeneous type.Dirección General de Investigación Científica y Técnic

Uncertainty principle estimates for vector fields

We derive weighted norm estimates for integral operators of potential type and for their related maximal operators. These operators are generalizations of the classical fractional integrals and fractional maximal functions. The norm estimates are derived in the context of a space of homogeneous type. The conditions required of the weight functions involve generalizations of the Fefferman-Phong "r-bump" condition. The results improve some earlier ones of the same kind, and they also extend to homogeneous spaces some estimates that were previously known to hold only in the classical Euclidean setting.Dirección General de Investigación Científica y TécnicaNational Science Foundatio

A sum operator with applications to self-improving properties of Poincaré inequalities in metric spaces

We define a class of summation operators with applications to the self-improving nature of Poincaré-Sobolev estimates, in fairly general quasimetric spaces of homogeneous type. We show that these sum operators play the familiar role of integral operators of potential type (e.g., Riesz fractional integrals) in deriving Poincaré-Sobolev estimates in cases when representations of functions by such integral operators are not readily available. In particular, we derive norm estimates for sum operators and use these estimates to obtain improved Poincaré-Sobolev results.University of BolognaGruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (Istituto Nazionale di Alta Matematica

Updating a map of sufficient conditions for the real nonnegative inverse eigenvalue problem

Producción CientíficaThe real nonnegative inverse eigenvalue problem (RNIEP) asks for necessary and sufficient conditions in order that a list of real numbers be the spectrum of a nonnegative real matrix. A number of sufficient conditions for the existence of such a matrix are known. The authors gave in a map of sufficient conditions establishing inclusion relations or independency relations between them. Since then new sufficient conditions for the RNIEP have appeared. In this paper we complete and update the map given in.Fondo Nacional de Desarrollo Científico y Tecnológico de Chile (project 1170313)Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (projects MTM2015-365764-C-1 / MTM2017-85996-R)Junta de Castilla y León (project VA128G18

Sharp weighted estimates for dyadic shifts and the A2 conjecture

We give a self-contained proof of the A2 conjecture, which claims that the norm of any Calderón–Zygmund operator is bounded by the first degree of the A2 norm of the weight. The original proof of this result by the first author relied on a subtle and rather difficult reduction to a testing condition by the last three authors. Here we replace this reduction by a new weighted norm bound for dyadic shifts – linear in the A2 norm of the weight and quadratic in the complexity of the shift –, which is based on a new quantitative two-weight inequality for the shifts. These sharp one- and two-weight bounds for dyadic shifts are the main new results of this paper. They are obtained by rethinking the corresponding previous results of Lacey-Petermichl-Reguera and Nazarov-Treil-Volberg. To complete the proof of the A2 conjecture, we also provide a simple variant of the representation, already in the original proof, of an arbitrary Calderón-Zygmund operator as an average of random dyadic shifts and random dyadic paraproducts. This method of the representation amounts to the refinement of the techniques from non-homogeneous Harmonic Analysis.Academy of FinlandConsejo Superior de Investigaciones CientíficasNational Science Foundatio

The first Paratropididae (Araneae, Mygalomorphae) from Colombia: new genus, species and records

The family of mygalomorph spiders Paratropididae Simon, 1889 is here reported for the first time for Colombia, where it is represented by three genera (Anisaspis, Paratropis, Stormtropis gen. n.) and eight species. One genus, Stormtropis, and six species constitute new taxa that are here diagnosed, described and illustrated. The geographical distribution of Paratropis papilligera FO Pickard-Cambridge, 1896 and Paratropis elicioi Dupérré, 2015 are also redescribed and expanded on the basis of new material examined. The diagnosis of the subfamily Paratropidinae, Paratropis Simon, 1889 and Anisaspis Simon, 1892 are emended including the variations of the new species. Likewise, a geographic distribution map for the entire family and a taxonomic key for the males of Paratropidinae are included. Other biogeographic, morphological, and taxonomic aspects are discussed

On universal realizability of spectra

Producción CientíficaA list Λ = {λ1, λ2, . . . , λn} of complex numbers is said to be realizable if it is the spectrum of an entrywise nonnegative matrix. The list Λ is said to be universally realizable (UR) if it is the spectrum of a nonnegative matrix for each possible Jordan canonical form allowed by Λ. It is well known that an n × n nonnegative matrix A is co-spectral to a nonnegative matrix B with constant row sums. In this paper, we extend the co-spectrality between A and B to a similarity between A and B, when the Perron eigenvalue is simple. We also show that if ǫ ≥ 0 and Λ = {λ1, λ2, . . . , λn} is UR, then {λ1 + ǫ, λ2, . . . , λn} is also UR. We give counter-examples for the cases: Λ = {λ1, λ2, . . . , λn} is UR implies {λ1 + ǫ, λ2 − ǫ, λ3, . . . , λn} is UR, and Λ1,Λ2 are UR implies Λ1 ∪ Λ2 is UR.Comisión Nacional de Investigación Científica y Tecnológica - Fondo Nacional de Desarrollo Científico y Tecnológico 1170313Comisión Nacional de Investigación Científica y Tecnológica - PAI 79160002Ministerio de Economía, Industria y Competitividad ( grants MTM2015-365764-C-1 / MTM2017-85996-R))Consejería de Educación de la Junta de Castilla y León (grant VA128G18

Evaluation of VIIRS Land Surface Temperature Using CREST-SAFE Air, Snow Surface, and Soil Temperature Data

In this study, the Visible Infrared Imager Radiometer Suite (VIIRS) Land Surface Temperature (LST) Environmental Data Record (EDR) was evaluated against snow surface (T-skin) and near-surface air temperature (T-air) ground observations recorded at the Cooperative Remote Sensing Science and Technology Center—Snow Analysis and Field Experiment (CREST-SAFE), located in Caribou, ME, USA during the winters of 2013 and 2014. The satellite LST corroboration of snow-covered areas is imperative because high-latitude regions are often physically inaccessible and there is a need to complement the data from the existing meteorological station networks. T-skin is not a standard meteorological parameter commonly observed at synoptic stations. Common practice is to measure surface infrared emission from the land surface at research stations across the world that allow for estimating ground-observed LST. Accurate T-skin observations are critical for estimating latent and sensible heat fluxes over snow-covered areas because the incoming and outgoing radiation fluxes from the snow mass and T-air make the snow surface temperature different from the average snowpack temperature. Precise characterization of the LST using satellite observations is an important issue because several climate and hydrological models use T-skin as input. Results indicate that T-air correlates better than T-skin with VIIRS LST data and that the accuracy of nighttime LST retrievals is considerably better than that of daytime. Based on these results, empirical relationships to estimate T-air and T-skin for clear-sky conditions from remotely-sensed (RS) LST were derived. Additionally, an empirical formula to correct cloud-contaminated RS LST was developed