366 research outputs found
Maximal directional operators along algebraic varieties
No full textWe establish the sharp growth order, up to epsilon losses, of the -norm of the maximal directional averaging operator along a finite subset of a polynomial variety of arbitrary dimension , in terms of cardinality. This is an extension of the works by Córdoba, for one-dimensional manifolds, Katz for the circle in two dimensions, and Demeter for the 2-sphere. For the case of directions on the two-dimensional sphere we improve by a factor of on the best known bound, due to Demeter, and we obtain a sharp estimate for our model operator. Our results imply new -estimates for Kakeya-type maximal functions with tubes pointing along polynomial directions. Our proof technique is novel and in particular incorporates an iterated scheme of polynomial partitioning on varieties adapted to directional operators, in the vein of Guth, Guth-Katz, and Zahl.34 pages, final version, incorporates the comments of the anonymous referees; to appear in Amer. J. Mat
A sharp estimate for the Hilbert transform along finite order lacunary sets of directions
No full textLet be a nonnegative integer and be a lacunary set of directions of order . We show that the norms, , of the maximal directional Hilbert transform in the plane are comparable to . For vector fields with range in a lacunary set of of order and generated using suitable combinations of truncations of Lipschitz functions, we prove that the truncated Hilbert transform along the vector field , is -bounded for all . These results extend previous bounds of the first author with Demeter, and of Guo and Thiele.20 pages, 2 figures. Submitted. Changes: clarified the definition of D-lacunary set and streamlined the notatio
Weighted inequalities and multiparameter harmonic analysis
No full textTesis descargada desde TESEOEl tema central de esta tesis es el estudio de desigualdades con pesos para algunos de los operadores clásicos del análisis armónico. De entre estos operadores, los que más nos interesan, son aquellos que son invariantes por dilataciones multiparamétricas. El principal representante de estos objetos es el operador maximal fuerte, elemento protagonista de esta tesis. Las dos cuestiones fundamentales que abordamos son las siguientes:
¿ Las propiedades de acotación de dichos operadores clásicos en espacios de Lebesgue con pesos. En particular, nos centramos en el estudio del problema de dos pesos para el operador maximal geométrico asociado a una cierta base general. Los resultados obtenidos se refieren fundamentalmente a las denominadas bases de Muckenhoupt, para las que se define una condición suficiente para el problema de dos pesos de tipo bump. Además, se estudia con detalle la desigualdad de Fefferman-Stein para el operador maximal fuerte. Finalmente, se caracteriza también el problema de un peso para estos operadores maximales generales en términos de condiciones débiles de tipo restringido.
¿ El cálculo preciso de la norma de estos operadores clásicos en función de la constante Ap del peso. Mostramos primero una estrategia para probar la optimalidad del exponente de la constante Ap del peso que evita el desarrollo de ejemplos específicos. Por último, aunque esta cuestión para el operador maximal fuerte continúa abierta, presentamos ciertos resultados parciales que se pueden entender como el primer paso hacia una teoría de pesos multiparamétrica cuantitativa.
La estructura de la tesis es la siguiente. Consta de cuatro capítulos juntos con una introducción donde se presentan los principales problemas encuadrados en su respectivo contexto histórico. El primero de estos capítulos describe las herramientas que son necesarias para la tesis. Los tres siguientes están dedicados a los cuatro problemas que se abordan en la tesis. Todos ellos cuentan con un apéndice donde se muestran algunas extensiones y cuestiones abiertas de dichos problemas.
Estos cuatro problemas principales junto con los teoremas que los resuelven se pueden encontrar en los siguientes artículos ya publicados:
- [LL12] Liguang Liu and Teresa Luque, A Bp condition for the strong maximal function, to appear in Trans.
Amer. Math. Soc. (2012).
- [LP14] Teresa Luque and Ioannis Parissis, The endpoint Fefferman-Stein inequality for the strong maximal function, J. Funct. Anal. 266 (2014), 199¿212.
- [HLP13] Paul A. Hagelstein, Teresa Luque, and Ioannis Parissis, Tauberian conditions, Muckenhoupt weights, and differentiation properties of weighted bases, to appear in Trans. Amer. Math. Soc (2013).
- [LPR13] Teresa Luque, Carlos Pérez, and Ezequiel Rela, Optimal exponents in weighted estimates without examples, to appear in Math. Res. Lett. (2013)
A metric approach to sparse domination
No full textWe present a general approach to sparse domination based on single-scale Lp-improving as a key assumption. The results are formulated in the setting of metric spaces of homogeneous type and avoid completely the use of dyadic-probabilistic techniques as well as of Christ–Hytönen–Kairema cubes. Among the applications of our general principle, we recover sparse domination of Dini-continuous Calderón–Zygmund kernels on spaces of homogeneous type, we prove a family of sparse bounds for maximal functions associated to convolutions with measures exhibiting Fourier decay, and we deduce sparse estimates for Radon transforms along polynomial submanifolds of Rn
The Dual Role of Echocardiography in the Diagnosis of Acute Cardiac Complications and Treatment Monitoring for Coronavirus Disease 2019 (COVID-19)
No full textThe Coronavirus Disease 2019 (COVID-19) pandemic, being caused by an easily and rapidly spreading novel betacoronavirus, has created a state of emergency for people, the scientific community, healthcare systems and states, while the global financial consequences are still unfolding. Cardiovascular complications have been reported for COVID-19-infected patients and are associated with a worse prognosis. ECG and biomarkers may raise suspicion of cardiac involvement. However, transthoracic echocardiography is a fast and reliable bedside method to establish the diagnosis of cardiac complications, including acute coronary syndromes, pericarditis, myocarditis, and pulmonary embolism. Early detection of cardiac dysfunction by speckle tracking echocardiography during off-line analysis may be used to identify a high-risk population for development of heart failure in the acute setting. Precautionary measures are mandatory for operators and equipment to avoid viral dispersion. No specific treatment is yet available for severe acute respiratory syndrome coronavirus 2 (SARS-CoV 2), and a variety of antiviral, immune-modifying, and antioxidant agents are therefore under intense investigation. Echocardiography, including assessment of myocardial deformation, may provide a useful tool to monitor the effects of the various treatment regimens on cardiac function both acutely and in the midterm. © Copyright © 2020 Vrettou, Parissis and Ikonomidis
Forty years literature review of primary lung lymphoma
No full textAbstract There are several unresolved issues through out the literature regarding the entity of primary lung lymphoma. Extensive literature review of this uncommon pathology is carried out. By taking into consideration the reported experience, the author discuss the classification, clinical features, histological differential diagnosis, prognostic criteria, therapeutic management and outcome of primary lung parenchyma lymphocytic infiltrates.</p
Pharmaco-economics of levosimendan in cardiology : A European perspective
No full textIntroduction: Heart failure places a significant economic burden on health care. Acute heart failure requires hospitalization and often frequent re-hospitalization in expensive wards where vasoactive rescue therapy is often added on top of standard medications. In these lean times, there is a growing need for cost-effective therapeutic options that supply superior support and in addition shorten the length of stay in hospital and reduce re-hospitalization rates. The inodilator levosimendan represents the latest addition to the vasoactive treatments of acute heart failure patients, and it appears to meet these expectations. Our aim was to answer the question whether the treatment efficacy of levosimendan - when selected as therapy for patients hospitalized for acute heart failure - brings savings to hospitals in various European countries representing different economies. Methods and results: We took a conservative approach and selected some a fortiori arguments to simplify the calculations. We selected seven European countries to represent different economies: Italy, Spain, Greece, Germany, Sweden, Finland and Israel. Data on the costs of medications and on the cost per day were collected and fed in a simple algorithm to detect savings. These saving varied from country to country, from a minimum of (sic)0.50 in Germany to a maximum of (sic)354.64 in Sweden. Conclusions: The use of levosimendan as a therapy for patients hospitalized for acute heart failure provides a net saving to hospitals driven by a reduction in the length of hospital stay. This finding is true in each of the countries considered in this study
Targeting the sympathetic nervous system with the selective imidazoline receptor agonist moxonidine for the management of hypertension: an international position statement
No full textHypertension is often linked with metabolic risk factors that share common pathophysiological pathways. Despite wide-spread availability of multiple drug classes, optimal blood pressure (BP) control remains challenging. Increased central sympathetic outflow is frequently neglected as a critical regulator of both circulatory and metabolic pathways and often remains unopposed therapeutically. Selective imidazoline receptor agonists (SIRAs) effectively reduce BP with a favorable side effect profile compared with older centrally acting antihypertensive drugs. Hard outcome data in hypertension, such as prevention of stroke, heart and kidney diseases, are not available with SIRAs. However, in direct comparisons, SIRAs were as effective as angiotensin-converting enzyme inhibitors, β-blockers, calcium channel blockers, and diuretics in lowering BP. Other beneficial effects on metabolic parameters in hypertensive patients with concomitant overweight and obesity have been documented with SIRAs. Here we review the existing evidence on the safety and efficacy of moxonidine, a widely available SIRA, compared with common antihypertensive agents and provide a consensus position statement based on inputs from 12 experts from Europe and Australia on SIRAs in hypertension management
The diagnostic approach and management of hypertension in the emergency department
No full textHypertension urgency and emergency represents a challenging condition in which clinicians should determine the assessment and/or treatment of these patients. Whether the elevation of blood pressure (BP) levels is temporary, in need of treatment, or reflects a chronic hypertensive state is not always easy to unravel. Unfortunately, current guidelines provide few recommendations concerning the diagnostic approach and treatment of emergency department patients presenting with severe hypertension. Target organ damage determines: the timeframe in which BP should be lowered, target BP levels as well as the drug of choice to use. It's important to distinguish hypertensive emergency from hypertensive urgency, usually a benign condition that requires more likely an outpatient visit and treatment
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