Harmonic Analysis Operators Associated with Multidimensional Bessel Operators

In this paper we establish that the maximal operator and the Littlewood-Paley g-function associated with the heat semigroup defined by multidimensional Bessel operators are of weak type (1,1). Also, we prove that Riesz transforms in the multidimensional Bessel setting are of strong type (p,p), for every $1<p<\infty$, and of weak type (1,1).Comment: 38 page

Hankel Multipliers of Laplace Transform Type

In this paper we prove that the Hankel multipliers of Laplace transform type on $(0,1)^n$ are of weak type (1,1). Also we analyze Lp-boundedness properties for the imaginary powers of Bessel operator on $(0,1)^n$.Comment: 32 page

Characterization of UMD Banach spaces by imaginary powers of Hermite and Laguerre operators

In this paper we characterize the Banach spaces with the UMD property by means of Lp-boundedness properties for the imaginary powers of the Hermite and Laguerre operators. In order to do this we need to obtain pointwise representations for the Laplace transform type multipliers associated with Hermite and Laguerre operators.Comment: 17 page

Square functions in the Hermite setting for functions with values in UMD spaces

In this paper we characterize the Lebesgue Bochner spaces $L^p(\mathbb{R}^n,B)$, $1<p<\infty$, by using Littlewood-Paley $g$-functions in the Hermite setting, provided that $B$ is a UMD Banach space. We use $\gamma$-radonifying operators $\gamma (H,B)$ where $H=L^2((0,\infty),\frac{dt}{t})$. We also characterize the UMD Banach spaces in terms of $L^p(\mathbb{R}^n,B)$-$L^p(\mathbb{R}^n,\gamma (H,B))$ boundedness of Hermite Littlewood-Paley $g$-functions

γ\gamma-radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces

In this paper we study Littlewood-Paley-Stein functions associated with the Poisson semigroup for the Hermite operator on functions with values in a UMD Banach space \B. If we denote by $H$ the Hilbert space L^2((0,\infty),dt/t),\gamma(H,\B) represents the space of $\gamma$-radonifying operators from $H$ into \B. We prove that the Hermite square function defines bounded operators from BMO_\mathcal{L}(\R,\B) (respectively, H^1_\mathcal{L}(\R, \B)) into BMO_\mathcal{L}(\R,\gamma(H,\B)) (respectively, H^1_\mathcal{L}(\R, \gamma(H,\B))), where $BMO_\mathcal{L}$ and $H^1_\mathcal{L}$ denote $BMO$ and Hardy spaces in the Hermite setting. Also, we obtain equivalent norms in BMO_\mathcal{L}(\R, \B) and H^1_\mathcal{L}(\R,\B) by using Littlewood-Paley-Stein functions. As a consequence of our results, we establish new characterizations of the UMD Banach spaces.Comment: 31 page

γ-Radonifying operators and UMD-valued Littlewood–Paley–Stein functions in the Hermite setting on BMO and Hardy spaces

AbstractIn this paper we study Littlewood–Paley–Stein functions associated with the Poisson semigroup for the Hermite operator on functions with values in a UMD Banach space B. If we denote by H the Hilbert space L2((0,∞),dt/t), γ(H,B) represents the space of γ-radonifying operators from H into B. We prove that the Hermite square function defines bounded operators from BMOL(Rn,B) (respectively, HL1(Rn,B)) into BMOL(Rn,γ(H,B)) (respectively, HL1(Rn,γ(H,B))), where BMOL and HL1 denote BMO and Hardy spaces in the Hermite setting. Also, we obtain equivalent norms in BMOL(Rn,B) and HL1(Rn,B) by using Littlewood–Paley–Stein functions. As a consequence of our results, we establish new characterizations of the UMD Banach spaces

A simple kinematic model for the Lagrangian description of relevant nonlinear processes in the stratospheric polar vortex

In this work, we study the Lagrangian footprint of the planetary waves present in the Southern Hemisphere stratosphere during the exceptional sudden Stratospheric warming event that took place during September 2002. Our focus is on constructing a simple kinematic model that retains the fundamental mechanisms responsible for complex fluid parcel evolution, during the polar vortex breakdown and its previous stages. The construction of the kinematic model is guided by the Fourier decomposition of the geopotential field. The study of Lagrangian transport phenomena in the ERA-Interim reanalysis data highlights hyperbolic trajectories, and these trajectories are Lagrangian objects that are the kinematic mechanism for the observed filamentation phenomena. Our analysis shows that the breaking and splitting of the polar vortex is justified in our model by the sudden growth of a planetary wave and the decay of the axisymmetric flow

A simple kinematic model for the Lagrangian description of relevant nonlinear processes in the stratospheric polar vortex

In this work, we study the Lagrangian footprint of the planetary waves present in the Southern Hemisphere stratosphere during the exceptional sudden Stratospheric warming event that took place during September 2002. Our focus is on constructing a simple kinematic model that retains the fundamental mechanisms responsible for complex fluid parcel evolution, during the polar vortex breakdown and its previous stages. The construction of the kinematic model is guided by the Fourier decomposition of the geopotential field. The study of Lagrangian transport phenomena in the ERA-Interim reanalysis data highlights hyperbolic trajectories, and these trajectories are Lagrangian objects that are the kinematic mechanism for the observed filamentation phenomena. Our analysis shows that the breaking and splitting of the polar vortex is justified in our model by the sudden growth of a planetary wave and the decay of the axisymmetric flow

Factors affecting mortality of shearwaters stranded by light pollution

Every year and across the world, thousands of fledglings of different petrel species crash into human structures because they are disorientated by artificial lights during their first flights. As this phenomenon is rather predictable, rescue cam- paigns are organized to help birds to reach the ocean, but unfortunately, a low proportion gets hurt or dies. Despite the huge number of affected individuals, and the fact that the problem was detected a long time ago, little is known on this source of mortality. We have studied the factors (i.e. body condition, plumage development, fledging date and sex) influencing the mortality of Cory’s Shearwa- ter Calonectris diomedea fledglings stranded inland due to light pollution in Ten- erife (Canary Islands) during two consecutive breeding seasons (2009 and 2010). Late fledglings showed lower values of a body condition index than early ones. No sex biases were detected, neither considering stranded birds overall, nor for recov- ery dates or in the body condition of rescued fledglings. Our results indicate that late birds stranded by lights showing abundant down are more susceptible to fatal collisions and that the lights do not selectively kill birds with lower body condition indices. An enhancement of veterinary care should be done during the last part of the fledging period when more fatal collisions occur, especially focused on fledg- lings with abundant down. More research to determine why some individuals end up disoriented around artificial lights and others do not is urgently needed to minimize or prevent fallouts.Peer reviewe