Variational inequalities in Hilbert spaces with measures and optimal stopping problems

We study the existence theory for parabolic variational inequalities in weighted L2 spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L2 setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coeficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.

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.

Homotopy exponents for large H-Spaces

We show that H-spaces with finitely generated cohomology, as an algebra or as an algebra over the Steenrod algebra, have homotopy exponents at all primes. This provides a positive answer to a question of Stanley.

Net spaces and boundedness of integral operators

In this paper we introduce new functional spaces which we call the net spaces. Using their properties, the necessary and sufficient conditions for the integral operators to be of strong or weak-type are obtained. The estimates of the norm of the convolution operator in weighted Lebesgue spaces are presented.

Convolution inequalities in Lorentz spaces

In this paper we study boundedness of the convolution operator in different Lorentz spaces. In particular, we obtain the limit case of the Young-O'Neil inequality in the classical Lorentz spaces. We also investigate the convolution operator in the weighted Lorentz spaces. Finally, norm inequalities for the potential operator are presented.

Norm convolution inequalities in Lebesgue spaces

We obtain upper and lower estimates of the (p; q) norm of the con-volution operator. The upper estimate sharpens the Young-type inequalities due to O'Neil and Stepanov.

Bergman-type singular operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

"Vegeu el resum a l'inici del document del fitxer adjunt."

Abstract splines in Krein spaces

"Vegeu el resum a l'inici del document del fitxer adjunt."

Trabecular Bone Score Helps Classifying Women At Riskof Fracture Prospectively In The Ofely Study

Objectives: Trabecular Bone Score (TBS, Med-Imaps, France) is an index of bone microarchitecture calculated from antero-posterior spine DXA scan and reported to be associated with fracture in prior case-control studies and in a large prospective study with the Prodigy DXA device. Our aim was to assess the ability of TBS to predict incident fracture and improve the classification of fracture prospectively in the OFELY study.Materials/Methods: TBS was assessed in 564 postmenopausal women (66±8 years old) from the OFELY cohort, who had a spine DXA scan (QDR 4500A, Hologic, USA) between year 2000 and 2001. During a mean follow up of 7.8±1.3 years, 94 women sustained a fragility fracture.Results: At the time of baseline DXA scan, women with incident fracture were significantly older (70±9 vs. 65± 8 years), had a lower spine BMD (T-score: −1.9±1.2 vs. −1.3±1.3, p<0.001) and spine TBS (−3.1%, p<0.001) than women without incident fracture. After adjustment for age, BMI and the presence of prevalent fracture, the magnitude of fracture prediction was similar for spine BMD (OR=1.42 [1.11;1.82] per SD decrease [95% CI]) and TBS (OR=1.34 [1.04;1.74]) but the combination of TBS and spine BMD did not improve fracture prediction. Spine BMD and TBS were both correlated with age (respectively r=−0.17 and −0.49, p<0.001) and correlated together with 39% of TBS explained by spine BMD (r=0.63, p<0.001). When using the WHO classification, 38% of the fractures occurred in osteoporotic (fracture rate=29%), 47% in osteopenic (fracture rate=16%) and 15% in women with T-score >−1 (fracture rate=9%). By classifying our population in tertiles of TBS, we found that 47% of the fractures occurred in the lowest tertile of TBS (fracture rate=23%) and 39% of the fracture that occurred in osteopenic women were in the lowest tertile of TBS.Conclusions: Spine BMD and TBS predicted fractures equally well. The addition of TBS to spine BMD added only limited information on fracture risk prediction in our cohort when considering the all range of BMD. Nevertheless combining the osteopenic T-score and the lowest TBS helped defining a subset of osteopenic women at higher risk of fracture.Disclosure of Interest: None declared.

Interpolation methods for stochastic processes spaces

In this paper the scales of classes of stochastic processes are introduced. New interpolation theorems and boundedness of some transforms of stochastic processes are proved. Interpolation method for generously-monotonous rocesses is entered. Conditions and statements of interpolation theorems concern he xed stochastic process, which diers from the classical results.

Hankel operators on holomorphic Hardy-Orlicz spaces

"Vegeu el resum a l'inici del document del fitxer adjunt."

Interpolation and sampling in small Bergman spaces

"Vegeu el resum a l'inici del document del fitxer adjunt."