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A. Eduardo Gatto

Publications and source records attributed to A. Eduardo Gatto.

6 recordsLinked to original sources
arXiv2012

Riesz Potentials, Bessel Potentials and Fractional Derivatives on Triebel-Lizorkin spaces for the Gaussian Measure

In a previous paper the boundedness properties of Riesz Potentials, Bessel potentials and Fractional Derivatives were studied in detail on Gaussian Besov-Lipschitz spaces $B_{p,q}^α(γ_d)$. In this paper we will continue our study proving the boundedness of those operators on Gaussian Triebel-Lizorkin spaces $F_{p,q}^α(γ_d)$. Also these results can be extended to the case of Laguerre or Jacobi expansions and even further to the general framework of diffusions semigroups.

math.CA↗
arXiv2008

Boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures

In the context of a finite measure metric space whose measure satisfies a growth condition, we prove "T1" type necessary and sufficient conditions for the boundedness of fractional integrals, singular integrals, and hypersingular integrals on inhomogeneous Lipschitz spaces. We also indicate how the results can be extended to the case of infinite measure. Finally we show applications to Real and Complex Analysis.

math.CT↗
arXiv2002

Boundedness properties of fractional integral operators associated to non--doubling measures

The main purpose of this paper is to investigate the behaviour of fractional integral operators associated to a measure on a metric space satisfying just a mild growth condition, namely that the measure of each ball is controlled by a fixed power of its radius. This allows, in particular, non--doubling measures. It turns out that this condition is enough to build up a theory that contains the classical results based upon the Lebesgue measure on euclidean space and their known extensions for doubling measures. We start by analyzing the images of the Lebesgue spaces associated to the measure. The Lipschitz spaces, defined in terms of the metric, play a basic role too. For a euclidean space equipped with one of these measures, we also consider the so-called `` regular\rq\rq $\bmo$ space introduced by X. Tolsa. We show that it contains the image of a Lebesgue space in the appropriate limit case and also that the image of the space `` regular\rq\rq $\bmo$ is contained in the adequate Lipschitz space.

math.FA↗