A generalization of the boundedness of certain integral operators in variable lebesgue spaces

Let n ε N. Let A1, ...Am be n×n invertible matrices. Let 0 ≤ α < n and 0 < αi < n such that α1 +...+αm = n-α . We define In [8] we obtained the boundedness of this operator from Lp(.)(Rn) into Lq(.)(Rn) for 1/q(.) = 1/p(.) - α/n, in the case that Ai is a power of certain fixed matrix A and for exponent functions p satisfying log-Hölder conditions and p(Ay) = p(y), y ε Rn. We will show now that the hypothesis on p, in certain cases, is necessary for the boundedness of Tα and we also prove the result for more general matrices Ai.Fil: Urciuolo, Marta. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Vallejos, Lucas Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

L p(·)–L q(·) boundedness of some integral operators obtained by extrapolation techniques

Given a matrix A such that AM = I and 0 ≤ α < n, for an exponent p satisfying p(Ax) = p(x) for a.e. x ∈ Rn, using extrapolation techniques,we obtain Lp(·) → Lq(·) boundedness, 1/q(·) = 1/p(·) - α/n, andweak type estimates for integral operators of the form Tαf(x) = ∫ f(y)|x - A1y|α1⋯|x - Amy|αm dy, where A1,⋯, Am are different powers of A such that Ai - Aj is invertible for i ≠ j, α1 + ⋯ + αm = n - α. We give some generalizations of these results.Fil: Urciuolo, Marta. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Vallejos, Lucas Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

Integral operators with rough kernels in variable Lebesgue spaces

We study integral operators with kernels K(x, y) = k1(x- A1y) ⋯ km(x- Amy) , ki(x)=Ωi(x)|x|n/qi where Ω i: Rn→ R are homogeneous functions of degree zero,satisfying a size and a Dini condition, Ai are certain invertible matrices, andnq1+⋯+nqm=n-α,0≤αFil: Urciuolo, Marta. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Vallejos, Lucas Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

Acotación de ciertos operadores integrales en espacios de Lebesgue variables

Tesis (Lic. en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2016.En el presente trabajo estudiamos la acotación de ciertos operadores integrales sobre los espacios de Lebesgue variables. En el capítulo I, damos los preliminares necesarios, en el II, comparamos las distintas técnicas con la que se obtiene la acotacion p - q de la Integral Fraccionaria. En el capítulo III mostramos resultados de la acotación p - q nuevamente de la Integral Fraccionaria pero con pesos A(p; q). En el capítulo IV introducimos los Operadores Integrales de Tipo Fraccionario, mostrando diferentes resultados de la continuidad en los espacios de Lebesgue clásicos y con pesos, en el V introducimos la teoría de los espacios de Lebesgue variables concluyendo con el estudio de la continuidad de la Integral Fraccionaria en dichos espacios y mostrando también un fuerte resultado sobre la función Maximal Sharp. Finalmente en el capítulo VI, volvemos a los Operadores Integrales de Tipo Fraccionario pero esta vez sobre los espacios de Lebesgue variables. Obtenemos resultados de acotación de tipo fuerte y débil para un caso particular de tales operadores.In this paper we study the boundedness of certain integral operators on variable Lebesgue spaces. The first chapter is devoted to preliminaries. In the second we compare the different techniques developed to get the p - q boundedness of the Fractional Integral Operator. In the third chapter we show weighted results about the Fractional Integral Operator. In the fourth chapter we define the Integral Operators of Fractional Type and we show resuts about the continuity os these operatos on classical and weighted Lebesgue spaces. In chapter V we describe the theory of Variable Lebesge Spaces and the boundedness of the Fractional Integral Operator on these spaces. Finally we obtain resuts about the boundedness of some Integral Operators of Fractional Type on variable Lebesgue spaces

Acotación de algunos operadores integrales entre espacios de Lebesgue variables

Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2020.En la presente tesis nos enfocamos en el estudio de algunos operadores integrales, en el contexto de los espacios de Lebesgue con exponente variable. Obtuvimos acotaciones estimaciones de tipo fuerte y de tipo débil para algunos operadores de tipo fraccionarios para funciones exponentes relacionadas con el núcleo del operador. También consideramos operadores de convolución con medidas sobre espacios euclídeos de dimensión n, soportadas sobre diferentes superficies singulares. Obtuvimos condiciones necesarias y suficientes para las funciones exponentes para obtener la acotación p-q del operador.In the present thesis we focus in the study of some integral operators, in the context of variable Lebesgue spaces. We obtain strong and weak type estimates for some fractional type operators for exponent functions related with the kernel of the operator. We also consider convolution operators with measures on n-dimensional euclidean spaces, supported on different singular surfaces. We obtain sufficient and also neccesary conditions for the exponents to get the p-q boundedness.Fil: Vallejos, Lucas Alejandro. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina

Canagliflozin and renal outcomes in type 2 diabetes and nephropathy

BACKGROUND Type 2 diabetes mellitus is the leading cause of kidney failure worldwide, but few effective long-term treatments are available. In cardiovascular trials of inhibitors of sodium–glucose cotransporter 2 (SGLT2), exploratory results have suggested that such drugs may improve renal outcomes in patients with type 2 diabetes. METHODS In this double-blind, randomized trial, we assigned patients with type 2 diabetes and albuminuric chronic kidney disease to receive canagliflozin, an oral SGLT2 inhibitor, at a dose of 100 mg daily or placebo. All the patients had an estimated glomerular filtration rate (GFR) of 30 to &lt;90 ml per minute per 1.73 m2 of body-surface area and albuminuria (ratio of albumin [mg] to creatinine [g], &gt;300 to 5000) and were treated with renin–angiotensin system blockade. The primary outcome was a composite of end-stage kidney disease (dialysis, transplantation, or a sustained estimated GFR of &lt;15 ml per minute per 1.73 m2), a doubling of the serum creatinine level, or death from renal or cardiovascular causes. Prespecified secondary outcomes were tested hierarchically. RESULTS The trial was stopped early after a planned interim analysis on the recommendation of the data and safety monitoring committee. At that time, 4401 patients had undergone randomization, with a median follow-up of 2.62 years. The relative risk of the primary outcome was 30% lower in the canagliflozin group than in the placebo group, with event rates of 43.2 and 61.2 per 1000 patient-years, respectively (hazard ratio, 0.70; 95% confidence interval [CI], 0.59 to 0.82; P=0.00001). The relative risk of the renal-specific composite of end-stage kidney disease, a doubling of the creatinine level, or death from renal causes was lower by 34% (hazard ratio, 0.66; 95% CI, 0.53 to 0.81; P&lt;0.001), and the relative risk of end-stage kidney disease was lower by 32% (hazard ratio, 0.68; 95% CI, 0.54 to 0.86; P=0.002). The canagliflozin group also had a lower risk of cardiovascular death, myocardial infarction, or stroke (hazard ratio, 0.80; 95% CI, 0.67 to 0.95; P=0.01) and hospitalization for heart failure (hazard ratio, 0.61; 95% CI, 0.47 to 0.80; P&lt;0.001). There were no significant differences in rates of amputation or fracture. CONCLUSIONS In patients with type 2 diabetes and kidney disease, the risk of kidney failure and cardiovascular events was lower in the canagliflozin group than in the placebo group at a median follow-up of 2.62 years

ATLANTIC BIRD TRAITS: a data set of bird morphological traits from the Atlantic forests of South America

Scientists have long been trying to understand why the Neotropical region holds the highest diversity of birds on Earth. Recently, there has been increased interest in morphological variation between and within species, and in how climate, topography, and anthropogenic pressures may explain and affect phenotypic variation. Because morphological data are not always available for many species at the local or regional scale, we are limited in our understanding of intra- and interspecies spatial morphological variation. Here, we present the ATLANTIC BIRD TRAITS, a data set that includes measurements of up to 44 morphological traits in 67,197 bird records from 2,790 populations distributed throughout the Atlantic forests of South America. This data set comprises information, compiled over two centuries (1820–2018), for 711 bird species, which represent 80% of all known bird diversity in the Atlantic Forest. Among the most commonly reported traits are sex (n = 65,717), age (n = 63,852), body mass (n = 58,768), flight molt presence (n = 44,941), molt presence (n = 44,847), body molt presence (n = 44,606), tail length (n = 43,005), reproductive stage (n = 42,588), bill length (n = 37,409), body length (n = 28,394), right wing length (n = 21,950), tarsus length (n = 20,342), and wing length (n = 18,071). The most frequently recorded species are Chiroxiphia caudata (n = 1,837), Turdus albicollis (n = 1,658), Trichothraupis melanops (n = 1,468), Turdus leucomelas (n = 1,436), and Basileuterus culicivorus (n = 1,384). The species recorded in the greatest number of sampling localities are Basileuterus culicivorus (n = 243), Trichothraupis melanops (n = 242), Chiroxiphia caudata (n = 210), Platyrinchus mystaceus (n = 208), and Turdus rufiventris (n = 191). ATLANTIC BIRD TRAITS (ABT) is the most comprehensive data set on measurements of bird morphological traits found in a biodiversity hotspot; it provides data for basic and applied research at multiple scales, from individual to community, and from the local to the macroecological perspectives. No copyright or proprietary restrictions are associated with the use of this data set. Please cite this data paper when the data are used in publications or teaching and educational activities. © 2019 The Authors. Ecology © 2019 The Ecological Society of Americ

ATLANTIC BIRD TRAITS

Scientists have long been trying to understand why the Neotropical region holds the highest diversity of birds on Earth. Recently, there has been increased interest in morphological variation between and within species, and in how climate, topography, and anthropogenic pressures may explain and affect phenotypic variation. Because morphological data are not always available for many species at the local or regional scale, we are limited in our understanding of intra- and interspecies spatial morphological variation. Here, we present the ATLANTIC BIRD TRAITS, a data set that includes measurements of up to 44 morphological traits in 67,197 bird records from 2,790 populations distributed throughout the Atlantic forests of South America. This data set comprises information, compiled over two centuries (1820–2018), for 711 bird species, which represent 80% of all known bird diversity in the Atlantic Forest. Among the most commonly reported traits are sex (n = 65,717), age (n = 63,852), body mass (n = 58,768), flight molt presence (n = 44,941), molt presence (n = 44,847), body molt presence (n = 44,606), tail length (n = 43,005), reproductive stage (n = 42,588), bill length (n = 37,409), body length (n = 28,394), right wing length (n = 21,950), tarsus length (n = 20,342), and wing length (n = 18,071). The most frequently recorded species are Chiroxiphia caudata (n = 1,837), Turdus albicollis (n = 1,658), Trichothraupis melanops (n = 1,468), Turdus leucomelas (n = 1,436), and Basileuterus culicivorus (n = 1,384). The species recorded in the greatest number of sampling localities are Basileuterus culicivorus (n = 243), Trichothraupis melanops (n = 242), Chiroxiphia caudata (n = 210), Platyrinchus mystaceus (n = 208), and Turdus rufiventris (n = 191). ATLANTIC BIRD TRAITS (ABT) is the most comprehensive data set on measurements of bird morphological traits found in a biodiversity hotspot; it provides data for basic and applied research at multiple scales, from individual to community, and from the local to the macroecological perspectives. No copyright or proprietary restrictions are associated with the use of this data set. Please cite this data paper when the data are used in publications or teaching and educational activities. © 2019 The Authors. Ecology © 2019 The Ecological Society of Americ

Effect of SGLT2 Inhibitors on Stroke and Atrial Fibrillation in Diabetic Kidney Disease: Results From the CREDENCE Trial and Meta-Analysis

BACKGROUND AND PURPOSE: Chronic kidney disease with reduced estimated glomerular filtration rate or elevated albuminuria increases risk for ischemic and hemorrhagic stroke. This study assessed the effects of sodium glucose cotransporter 2 inhibitors (SGLT2i) on stroke and atrial fibrillation/flutter (AF/AFL) from CREDENCE (Canagliflozin and Renal Events in Diabetes With Established Nephropathy Clinical Evaluation) and a meta-analysis of large cardiovascular outcome trials (CVOTs) of SGLT2i in type 2 diabetes mellitus.METHODS: CREDENCE randomized 4401 participants with type 2 diabetes mellitus and chronic kidney disease to canagliflozin or placebo. Post hoc, we estimated effects on fatal or nonfatal stroke, stroke subtypes, and intermediate markers of stroke risk including AF/AFL. Stroke and AF/AFL data from 3 other completed large CVOTs and CREDENCE were pooled using random-effects meta-analysis.RESULTS: In CREDENCE, 142 participants experienced a stroke during follow-up (10.9/1000 patient-years with canagliflozin, 14.2/1000 patient-years with placebo; hazard ratio [HR], 0.77 [95% CI, 0.55-1.08]). Effects by stroke subtypes were: ischemic (HR, 0.88 [95% CI, 0.61-1.28]; n=111), hemorrhagic (HR, 0.50 [95% CI, 0.19-1.32]; n=18), and undetermined (HR, 0.54 [95% CI, 0.20-1.46]; n=17). There was no clear effect on AF/AFL (HR, 0.76 [95% CI, 0.53-1.10]; n=115). The overall effects in the 4 CVOTs combined were: total stroke (HRpooled, 0.96 [95% CI, 0.82-1.12]), ischemic stroke (HRpooled, 1.01 [95% CI, 0.89-1.14]), hemorrhagic stroke (HRpooled, 0.50 [95% CI, 0.30-0.83]), undetermined stroke (HRpooled, 0.86 [95% CI, 0.49-1.51]), and AF/AFL (HRpooled, 0.81 [95% CI, 0.71-0.93]). There was evidence that SGLT2i effects on total stroke varied by baseline estimated glomerular filtration rate (P=0.01), with protection in the lowest estimated glomerular filtration rate (&lt;45 mL/min/1.73 m2]) subgroup (HRpooled, 0.50 [95% CI, 0.31-0.79]).CONCLUSIONS: Although we found no clear effect of SGLT2i on total stroke in CREDENCE or across trials combined, there was some evidence of benefit in preventing hemorrhagic stroke and AF/AFL, as well as total stroke for those with lowest estimated glomerular filtration rate. Future research should focus on confirming these data and exploring potential mechanisms. Registration: URL: https://www.clinicaltrials.gov; Unique identifier: NCT02065791