Sharp weighted bounds for fractional integral operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.

On moduli of smoothness of fractional order

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

A rotation method which gives linear Lp-Estimates for powers of the Ahlfors-Beurling operator

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Large deviation for BSDE with subdifferential operator

In this paper we prove that the solution of a backward stochastic differential equation, which involves a subdifferential operator and associated to a family of reflecting diffusion processes, converges to the solution of a deterministic backward equation and satisfes a large deviation principle.

On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

HSU-Robbins and Spitzer's theorems for the variations of fractional Brownian motion

Using recent results on the behavior of multiple Wiener-Itô integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.

On a supremum operator

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On spectral properties of the modified convolution operator

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On separation of a degenerate differential operator in Hilbert space

A coercive estimate for a solution of a degenerate second order di fferential equation is installed, and its applications to spectral problems for the corresponding dif ferential operator is demonstrated. The suffi cient conditions for existence of the solutions of one class of the nonlinear second order diff erential equations on the real axis are obtained.

Operator expansion: definition and molecular integral applications

Es defineix l'expansió general d'operadors com una combinació lineal de projectors i s'exposa la seva aplicació generalitzada al càlcul d'integrals moleculars. Com a exemple numèric, es fa l'aplicació al càlcul d'integrals de repulsió electrònica entre quatre funcions de tipus s centrades en punts diferents, i es mostren tant resultats del càlcul com la definició d'escalat respecte a un valor de referència, que facilitarà el procés d'optimització de l'expansió per uns paràmetres arbitraris. Es donen resultats ajustats al valor exacte

Operator algebras: an informal overview

This article is an informal introduction to some classical results of the theory of operator algebras. It aims to illustrate the richness and diversity of possible applications of this topic.

Hours worked - Productivity puzzle: identification in fractional integration settings

A recent finding of the structural VAR literature is that the response of hours worked to a technology shock depends on the assumption on the order of integration of the hours. In this work we relax this assumption, allowing for fractional integration and long memory in the process for hours and productivity. We find that the sign and magnitude of the estimated impulse responses of hours to a positive technology shock depend crucially on the assumptions applied to identify them. Responses estimated with short-run identification are positive and statistically significant in all datasets analyzed. Long-run identification results in negative often not statistically significant responses. We check validity of these assumptions with the Sims (1989) procedure, concluding that both types of assumptions are appropriate to recover the impulse responses of hours in a fractionally integrated VAR. However, the application of longrun identification results in a substantial increase of the sampling uncertainty. JEL Classification numbers: C22, E32. Keywords: technology shock, fractional integration, hours worked, structural VAR, identification

A total order in [0,1] defined through a 'next' operator

A `next' operator, s, is built on the set R1=(0,1]-{ 1-1/e} defining a partial order that, with the help of the axiom of choice, can be extended to a total order in R1. Besides, the orbits {sn(a)}nare all dense in R1 and are constituted by elements of the samearithmetical character: if a is an algebraic irrational of degreek all the elements in a's orbit are algebraic of degree k; if a istranscendental, all are transcendental. Moreover, the asymptoticdistribution function of the sequence formed by the elements in anyof the half-orbits is a continuous, strictly increasing, singularfunction very similar to the well-known Minkowski's ?(×) function.

Is the observed persistence spurious? A test for fractional integration versus short memory and structural breaks

Although it is commonly accepted that most macroeconomic variables are nonstationary, it is often difficult to identify the source of the non-stationarity. In particular, it is well-known that integrated and short memory models containing trending components that may display sudden changes in their parameters share some statistical properties that make their identification a hard task. The goal of this paper is to extend the classical testing framework for I(1) versus I(0)+ breaks by considering a a more general class of models under the null hypothesis: non-stationary fractionally integrated (FI) processes. A similar identification problem holds in this broader setting which is shown to be a relevant issue from both a statistical and an economic perspective. The proposed test is developed in the time domain and is very simple to compute. The asymptotic properties of the new technique are derived and it is shown by simulation that it is very well-behaved in finite samples. To illustrate the usefulness of the proposed technique, an application using inflation data is also provided.

The induced generalized OWA operator

[spa] Se presenta el operador OWA generalizado inducido (IGOWA). Es un nuevo operador de agregación que generaliza al operador OWA a través de utilizar las principales características de dos operadores muy conocidos como son el operador OWA generalizado y el operador OWA inducido. Entonces, este operador utiliza medias generalizadas y variables de ordenación inducidas en el proceso de reordenación. Con esta formulación, se obtiene una amplia gama de operadores de agregación que incluye a todos los casos particulares de los operadores IOWA y GOWA, y otros casos particulares. A continuación, se realiza una generalización mayor al operador IGOWA a través de utilizar medias cuasi-aritméticas. Finalmente, también se desarrolla un ejemplo numérico del nuevo modelo en un problema de toma de decisiones financieras.