UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces

We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square functions associated with Poisson semigroups for Bessel operators are defined by using fractional derivatives. If B is a UMD Banach space we obtain for B-valued Hardy and BMO spaces equivalent norms involving $\gamma$-radonifying operators and square functions. We also establish characterizations of UMD Banach spaces by using Hardy and BMO-boundedness properties of g-functions associated to Bessel-Poisson semigroup

UMD Banach spaces and square functions associated with heat semigroups for Schr\"odinger and Laguerre operators

In this paper we define square functions (also called Littlewood-Paley-Stein functions) associated with heat semigroups for Schr\"odinger and Laguerre operators acting on functions which take values in UMD Banach spaces. We extend classical (scalar) L^p-boundedness properties for the square functions to our Banach valued setting by using \gamma-radonifying operators. We also prove that these L^p-boundedness properties of the square functions actually characterize the Banach spaces having the UMD property

LpL^p-boundedness properties for the maximal operators for semigroups associated with Bessel and Laguerre operators

In this paper we prove that the generalized (in the sense of Caffarelli and Calder\'on) maximal operators associated with heat semigroups for Bessel and Laguerre operators are weak type (1,1). Our results include other known ones and our proofs are simpler than the ones for the known special cases.Comment: 8 page

Children’s improvement of a motor response during backward falls through the implementation of a safe fall program

The World Health Organization has warned that, in children, the second cause of death from unintentional injuries are falls. The objective of this study was to analyze the motor response of primary schoolchildren when a backwards fall occurs. These analyses occurred before and after interventions of the Safe Fall program, which aims to teach safe and protected ways of backward falling. A quasi-experimental research design was used, with a sample of 122 Spanish (Sevillian) schoolchildren in the 10–12 age bracket. The INFOSECA ad-hoc observation scale was used for data collection: this scale registers 5 essential physical reactions throughout the process of a safe and protected backwards fall. After that, a number of descriptive, correlational and contrast statistics were applied. The value used in the McNemar test to establish statistical significance was p < 0.05. Results showed that over 85% of students had developed the competence to correctly perform all five physical motions that allow for a safer backward fall. The teaching of safe and protected techniques for falling backwards in child population in Primary Education is possible through the implementation of the Safe Fall program in Physical Education classes, which can help making falls safer, diminishing the risk and severity of the injuries they cause

Phosphorylation of Thr9 Affects the Folding Landscape of the N-Terminal Segment of Human AGT Enhancing Protein Aggregation of Disease-Causing Mutants

The mutations G170R and I244T are the most common disease cause in primary hyperoxaluria type I (PH1). These mutations cause the misfolding of the AGT protein in the minor allele AGT-LM that contains the P11L polymorphism, which may affect the folding of the N-terminal segment (NTT-AGT). The NTT-AGT is phosphorylated at T9, although the role of this event in PH1 is unknown. In this work, phosphorylation of T9 was mimicked by introducing the T9E mutation in the NTT-AGT peptide and the full-length protein. The NTT-AGT conformational landscape was studied by circular dichroism, NMR, and statistical mechanical methods. Functional and stability effects on the full-length AGT protein were characterized by spectroscopic methods. The T9E and P11L mutations together reshaped the conformational landscape of the isolated NTT-AGT peptide by stabilizing ordered conformations. In the context of the full-length AGT protein, the T9E mutation had no effect on the overall AGT function or conformation, but enhanced aggregation of the minor allele (LM) protein and synergized with the mutations G170R and I244T. Our findings indicate that phosphorylation of T9 may affect the conformation of the NTT-AGT and synergize with PH1-causing mutations to promote aggregation in a genotype-specific manner. Phosphorylation should be considered a novel regulatory mechanism in PH1 pathogenesis.Comunidad Valenciana CIAICO/2021/135 AULA FUNCANIS-UGRERDF/Spanish Ministry of Science, Innovation, and Universities-State Research Agency RTI2018-096246-B-I00Junta de Andalucia P18-RT-2413 ERDF/ Counseling of Economic transformation, Industry, Knowledge, and Universities B-BIO-84-UGR2

γ-Radonifying operators and UMD-valued Littlewood–Paley–Stein functions in the Hermite setting on BMO and Hardy spaces

AbstractIn this paper we study Littlewood–Paley–Stein functions associated with the Poisson semigroup for the Hermite operator on functions with values in a UMD Banach space B. If we denote by H the Hilbert space L2((0,∞),dt/t), γ(H,B) represents the space of γ-radonifying operators from H into B. We prove that the Hermite square function defines bounded operators from BMOL(Rn,B) (respectively, HL1(Rn,B)) into BMOL(Rn,γ(H,B)) (respectively, HL1(Rn,γ(H,B))), where BMOL and HL1 denote BMO and Hardy spaces in the Hermite setting. Also, we obtain equivalent norms in BMOL(Rn,B) and HL1(Rn,B) by using Littlewood–Paley–Stein functions. As a consequence of our results, we establish new characterizations of the UMD Banach spaces

Carbon and oxygen in HII regions of the Magellanic Clouds: abundance discrepancy and chemical evolution

We present C and O abundances in the Magellanic Clouds derived from deep spectra of HII regions. The data have been taken with the Ultraviolet-Visual Echelle Spectrograph at the 8.2-m VLT. The sample comprises 5 HII regions in the Large Magellanic Cloud (LMC) and 4 in the Small Magellanic Cloud (SMC). We measure pure recombination lines (RLs) of CII and OII in all the objects, permitting to derive the abundance discrepancy factors (ADFs) for O^2+, as well as their O/H, C/H and C/O ratios. We compare the ADFs with those of other HII regions in different galaxies. The results suggest a possible metallicity dependence of the ADF for the low-metallicity objects, but more uncertain for high-metallicity objects. We compare nebular and B-type stellar abundances and we find that the stellar abundances agree better with the nebular ones derived from collisionally excited lines (CELs). Comparing these results with other galaxies we observe that stellar abundances seem to agree better with the nebular ones derived from CELs in low-metallicity environments and from RLs in high-metallicity environments. The C/H, O/H and C/O ratios show almost flat radial gradients, in contrast with the spiral galaxies where such gradients are negative. We explore the chemical evolution analysing C/O vs. O/H and comparing with the results of HII regions in other galaxies. The LMC seems to show a similar chemical evolution to the external zones of small spiral galaxies and the SMC behaves as a typical star-forming dwarf galaxy.Comment: Accepted for publication in MNRAS, 17 pages, 11 figures, 8 table

A choice of Sobolev spaces associated with ultraspherical expansions

We discuss two possible definitions for Sobolev spaces associated with ultraspherical expansions. These definitions depend on the notion of higher order derivative. We show that in order to have an isomorphism between Sobolev and potential spaces, the higher order derivatives to be considered are not the iteration of the first order derivatives. Some discussions about higher order Riesz transforms are involved. Also we prove that the maximal operator for the Poisson integral in the ultraspherical setting is bounded on the Sobolev spaces