arXiv subjects

Lourdes Rodríguez-Mesa

Publications and source records attributed to Lourdes Rodríguez-Mesa.

24 records · Page 2Linked to original sources

arXiv2012

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 $γ$-radonifying operators $γ(H,B)$ where $H=L^2((0,\infty),\frac{dt}{t})$. We also characterize the UMD Banach spaces in terms of $L^p(\mathbb{R}^n,B)$-$L^p(\mathbb{R}^n,γ(H,B))$ boundedness of Hermite Littlewood-Paley $g$-functions.

math.CA↗

arXiv2012

$L^p$-boundedness properties for the maximal operators for semigroups associated with Bessel and Laguerre operators

In this paper we prove that the generalized (in the sense of Caffarelli and Calderón) maximal operators associated with heat semigroups for Bessel and Laguerre operators are weak type (1,1). Our results include other known ones and our proofs are simpler than the ones for the known special cases.

math.CA↗

arXiv2011

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 $γ$-radonifying norms. Also we prove that the UMD Banach spaces are the unique Banach spaces for which certain $γ$-radonifying Carleson inequalities for Bessel-Poisson integrals of $BMO_o(\mathbb{R},X)$ functions hold.

math.CA↗

arXiv2011

Characterization of uniformly convex and smooth Banach spaces by using Carleson measures in Bessel settings

In this paper we obtain new characterizations of the q-uniformly convex and smooth Banach spaces by using Carleson measures. These measures are defined by Poisson integral associated with Bessel operators and Banach valued BMO-functions. By the way we describe q-uniformly convexity and smoothness of a Banach space in terms of the mapping properties of the Lusin integral defined by the Poisson semigroup for Bessel operators.

math.CA↗

arXiv2011

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.

math.CA↗

arXiv2010

Higher order Riesz transforms in the ultraspherical setting as principal value integral operators

In this paper we represent the $k$-th Riesz transform in the ultraspherical setting as a principal value integral operator for every $k\in \mathbb{N}$. We also measure the speed of convergence of the limit by proving $L^p$-boundedness properties for the oscillation and variation operators associated with the corresponding truncated operators.

math.CA↗