Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions

In this paper we consider the space $BMO_o(\mathbb{R},X)$ of bounded mean oscillations and odd functions on $\mathbb{R}$ taking values in a UMD Banach space $X$. The functions in $BMO_o(\mathbb{R},X)$ are characterized by Carleson type conditions involving Bessel convolutions and $\gamma$-radonifying norms. Also we prove that the UMD Banach spaces are the unique Banach spaces for which certain $\gamma$-radonifying Carleson inequalities for Bessel-Poisson integrals of $BMO_o(\mathbb{R},X)$ functions hold.Comment: 29 page

Indefinición terminológica y tecnología educativa

El propósito de este trabajo es analizar los problemas de la indefinición terminológica en el campo de la tecnología educativa, visibles tanto en las conceptualizaciones y clasificacio- nes existentes sobre medios y materiales como en la propia práctica educativa. Expondre- mos, en primer lugar, los1 motivos de esta preocupación. Atenderemos, en segundo lugar, a las manifestaciones y los contextos especifícos donde se manifiesta esa indefinición. A continuación presentaremos un ejemplo concreto de esta «nubosidad terminológica» y el modo como nos enfrentamos al problema.This paper analysis the consequences deriving from the lack of clear and consistent terminology in the field of Educational Technology. The terminological problems reviewed were encountered during research for a study on the percepcion of teachers regarding curricular materials published as a result of the Educational Reform in Galicia (Spain). Examples are given of confusion in questionnaires, interviews, and scientific literature, and suggestions for clarification are provided. We conclude with some general considerations and recommendations on this topic

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

La transformación integral y la convolución de Hankel de funciones y distribuciones

Se investiga la convergencia puntual de las integrales parciales de Hankel. Se introducen los llamados espacios de Lipschitz-Hankel y de Besov-Hankel, que son caracterizados mediante las integrales parciales de Hankel y las medias de Bochner-Riesz. Se discute la integrabilidad de las transformadas de Hankel de funciones en oportunos espacios de Lipschitz-Hankel. Se analiza el comportamiento de la transformación y la convolucion de hankel sobre distribuciones de crecimiento exponencial. Se consideran las ecuaciones de convolución hankel en espacios de funciones generalizadas de crecimiento lento y exponencial, introduciendo el concepto de hipoelipticidad para los operadores de convolución hankel y caracterizándolo a través del crecimiento de la transformada de hankel de tales operadores. Se introducen nuevos espacios de distribuciones transformables hankel, que son identificados con cierta clase de operadores que conmutan con la convolución de Hanke

Variable exponent Hardy spaces associated with discrete Laplacians on graphs

In this paper we develop the theory of variable exponent Hardy spaces associated with discrete Laplacians on infinite graphs. Our Hardy spaces are defined by square integrals, atomic and molecular decompositions. Also we study boundedness properties of Littlewood-Paley functions, Riesz transforms, and spectral multipliers for discrete Laplacians on variable exponent Hardy spaces

Discrete harmonic analysis associated with ultraspherical expansions

We study discrete harmonic analysis associated with ultraspherical orthogonal functions. We establish weighted l^p-boundedness properties of maximal operators and Littlewood-Paley g-functions defined by Poisson and heat semigroups generated by certain difference operator. We also prove weighted l^p-boundedness properties of transplantation operators associated to the system of ultraspherical functions. In order to show our results we previously establish a vector-valued local Calder\'on-Zygmund theorem in our discrete setting