The Constant of Interpolation in Bloch Type Spaces

It is known that there exists a constant 0 < Δ1 < 1 such that any Δ1-separated sequence for the pseudohyperbolic distance in the open unit disk D of C is interpolating for the classical Bloch space B. We will prove that 0.8114 < Δ1 < 0.9785 and we will also generalize this result for Bloch type spaces Bvp for vp(z) = (1−|z| 2) p. In particular, we will provide a construction to calculate an estimate of the lower and upper bounds for the corresponding constant of separation Δp for these spaces. We also prove that Δp tends to 1 when p → ∞.Funding for open access charge: CRUE-Universitat Jaume

Effect of allopurinol in addition to hypothermia treatment in neonates for hypoxic-ischemic brain injury on neurocognitive outcome (ALBINO): Study protocol of a blinded randomized placebo-controlled parallel group multicenter trial for superiority (phase III)

Background: Perinatal asphyxia and resulting hypoxic-ischemic encephalopathy is a major cause of death and long-term disability in term born neonates. Up to 20,000 infants each year are affected by HIE in Europe and even more in regions with lower level of perinatal care. The only established therapy to improve outcome in these infants is therapeutic hypothermia. Allopurinol is a xanthine oxidase inhibitor that reduces the production of oxygen radicals as superoxide, which contributes to secondary energy failure and apoptosis in neurons and glial cells after reperfusion of hypoxic brain tissue and may further improve outcome if administered in addition to therapeutic hypothermia. Methods: This study on the effects of ALlopurinol in addition to hypothermia treatment for hypoxic-ischemic Brain Injury on Neurocognitive Outcome (ALBINO), is a European double-blinded randomized placebo-controlled parallel group multicenter trial (Phase III) to evaluate the effect of postnatal allopurinol administered in addition to standard of care (including therapeutic hypothermia if indicated) on the incidence of death and severe neurodevelopmental impairment at 24 months of age in newborns with perinatal hypoxic-ischemic insult and signs of potentially evolving encephalopathy. Allopurinol or placebo will be given in addition to therapeutic hypothermia (where indicated) to infants with a gestational age 65 36 weeks and a birth weight 65 2500 g, with severe perinatal asphyxia and potentially evolving encephalopathy. The primary endpoint of this study will be death or severe neurodevelopmental impairment versus survival without severe neurodevelopmental impairment at the age of two years. Effects on brain injury by magnetic resonance imaging and cerebral ultrasound, electric brain activity, concentrations of peroxidation products and S100B, will also be studied along with effects on heart function and pharmacokinetics of allopurinol after iv-infusion. Discussion: This trial will provide data to assess the efficacy and safety of early postnatal allopurinol in term infants with evolving hypoxic-ischemic encephalopathy. If proven efficacious and safe, allopurinol could become part of a neuroprotective pharmacological treatment strategy in addition to therapeutic hypothermia in children with perinatal asphyxia. Trial registration: NCT03162653, www.ClinicalTrials.gov, May 22, 2017

On interpolating sequences for Bloch type spaces

When we deal with , it is known that interpolating sequences are interpolating and it is sufficient to interpolate idempotents of in order to interpolate the whole . We will extend these results to the frame of interpolating sequences for Bloch type spaces and study the connection between the interpolating operators on and . Furthermore, for some particular weights v, we will provide examples of interpolating sequences for whose constant of separation is as close to 0 as desired

On interpolating sequences for Bloch type spaces

When we deal with , it is known that interpolating sequences are interpolating and it is sufficient to interpolate idempotents of in order to interpolate the whole . We will extend these results to the frame of interpolating sequences for Bloch type spaces and study the connection between the interpolating operators on and . Furthermore, for some particular weights v, we will provide examples of interpolating sequences for whose constant of separation is as close to 0 as desired.Funding for open access charge: CRUE-Universitat Jaume