Lourdes Rodríguez-Mesa

A CHOICE OF SOBOLEV SPACES ASSOCIATED WITH ULTRASPHERICAL EXPANSIONS

We discuss two possible definitions for Sobolev spaces associated with ultraspherical expansions. These definitions depend on the notion of higher order derivative. We show that in order to have an isomorphism between Sobolev and potential spaces, the higher order derivatives to be considered are not the iteration of the first order derivatives. Some discussions about higher order Riesz transforms are involved. Also we prove that the maximal operator for the Poisson integral in the ultraspherical setting is bounded on the Sobolev spaces.

Anisotropic Hardy-Lorentz Spaces with Variable Exponents

In this paper we introduce Hardy-Lorentz spaces with variable exponents associated to dilation in

Square functions and spectral multipliers for Bessel operators in UMD spaces

{\Bbb R}^n

Weak type (1,1) estimates for Caffarelli-Calderón generalized maximal operators for semigroups associated with Bessel and Laguerre operators

. We establish maximal characterizations and atomic decompositions for our variable exponent anisotropic Hardy-Lorentz spaces.

Variable exponent Hardy spaces associated with discrete Laplacians on graphs

In this paper, we consider square functions (also called Littlewood-Paley g-functions) associated to Hankel convolutions acting on functions in the Bochner Lebesgue space L-p((0, infinity), B), whe ...

Molecules Associated to Hardy Spaces with Pointwise Variable Anisotropy

is bounded from L(Ω, μ) into itself, for every 1 < p < ∞. As far as we know there is not a result showing the behavior of T∗ on L (Ω, μ) for every diffusion semigroup {Tt}t>0. The behavior of T∗ on L(Ω, μ) must be established by taking into account the intrinsic properties of {Tt}t>0. The usual result says that T∗ is bounded from L(Ω, μ) into L1,∞(Ω, μ), but not bounded from L(Ω, μ) into L(Ω, μ). In order to analyze T∗ in L (Ω, μ), in many cases this maximal operator is controlled by a Hardy-Littlewood type maximal operator, and also, the vector valued CalderónZygmund theory ([14]) can be used. These procedures have been employed to study the maximal operators associated to the classical heat semigroup [17, p. 57], to Hermite operators ([10], [15] and [20]), to Laguerre operators ([8], [9], [10], [13] and [19]), to Bessel operators ([1], [2], [3], [11] and [18]) and to Jacobi operators ([11] and [12]), amongst others.

Hankel convolution on distribution spaces with exponential growth

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.

Transference between Laguerre and Hermite settings

In this paper we introduce molecules associated to Hardy spaces with pointwise variable anisotropy. We establish molecular characterizations of such Hardy spaces with pointwise variable anisotropy.