Calder\'on-Zygmund operators in the Bessel setting

We study several fundamental operators in harmonic analysis related to Bessel operators, including maximal operators related to heat and Poisson semigroups, Littlewood-Paley-Stein square functions, multipliers of Laplace transform type and Riesz transforms. We show that these are (vector-valued) Calder\'on-Zygmund operators in the sense of the associated space of homogeneous type, and hence their mapping properties follow from the general theory.Comment: 21 page

UMD Banach spaces and the maximal regularity for the square root of several operators

In this paper we prove that the maximal $L^p$-regularity property on the interval $(0,T)$, $T>0$, for Cauchy problems associated with the square root of Hermite, Bessel or Laguerre type operators on $L^2(\Omega, d\mu; X),$ characterizes the UMD property for the Banach space $X$.Comment: 23 pages. To appear in Semigroup Foru

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

On the maximal function for the generalized Ornstein-Uhlenbeck semigroup

In this note we consider the maximal function for the generalized Ornstein-Uhlenbeck semigroup in \RR associated with the generalized Hermite polynomials $\{H_n^{\mu}\}$ and prove that it is weak type (1,1) with respect to $d\lambda_{\mu}(x) = |x|^{2\mu}e^{-|x|^2} dx,$ for $\mu >-1/2$ as well as bounded on $L^p(d\lambda_\mu)$ for $p>1$Comment: 10 pages. See also http://euler.ciens.ucv.ve/~wurbina/preprints.htm

Anisotropic weak hardy spaces and wavelets

We characterize the anisotropic weak Hardy spacesHp,∞A (Rn) associated with an expansive matrix A by using square functions involving wavelets coefficientsB. Barrios is partially supported by MTM2010-16518 and J. J. Betancor is partially supported by MTM2010-1797

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

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