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J. C. Fariña

Publications and source records attributed to J. C. Fariña.

6 recordsLinked to original sources
arXiv2021

Littlewood-Paley-Stein theory and Banach spaces in the inverse Gaussian setting

In this paper we consider Littlewood-Paley functions defined by the semigroups associated with the operator $\mathcal{A}=-\fracΔ{2}-x\nabla$ in the inverse Gaussian setting for Banach valued functions. We characterize the uniformly convex and smooth Banach spaces by using $L^p(\mathbb{R}^n,γ_{-1})$- properties of the $\mathcal{A}$-Littlewood-Paley functions. We also use Littlewood-Paley functions associated with $\mathcal{A}$ to characterize the Köthe function spaces with the UMD property.

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arXiv2014

Vector valued multivariate spectral multipliers, Littlewood-Paley functions, and Sobolev spaces in hte Hermite setting

In this paper we find new equivalent norms in $L^p(\mathbb{R}^n,\mathbb{B})$ by using multivariate Littlewood-Paley functions associated with Poisson semigroup for the Hermite operator, provided that $\mathbb{B}$ is a UMD Banach space with the property ($α$). We make use of $γ$-radonifying operators to get new equivalent norms that allow us to obtain $L^p(\mathbb{R}^n,\mathbb{B})$-boundedness properties for (vector valued) multivariate spectral multipliers for Hermite operators. As application of this Hermite multiplier theorem we prove that the Banach valued Hermite Sobolev and potential spaces coincide.

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arXiv2012

UMD Banach spaces and square functions associated with heat semigroups for Schrödinger and Laguerre operators

In this paper we define square functions (also called Littlewood-Paley-Stein functions) associated with heat semigroups for Schrödinger and Laguerre operators acting on functions which take values in UMD Banach spaces. We extend classical (scalar) L^p-boundedness properties for the square functions to our Banach valued setting by using γ-radonifying operators. We also prove that these L^p-boundedness properties of the square functions actually characterize the Banach spaces having the UMD property.

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arXiv2011

A T1 criterion for Hermite-Calderon-Zygmund operators on the BMO_H(R^n) space and applications

In this paper we establish a T1 criterion for the boundedness of Hermite-Calderon-Zygmund operators on the BMO_H(R^n) space naturally associated to the Hermite operator H. We apply this criterion in a systematic way to prove the boundedness on BMO_H(R^n) of certain harmonic analysis operators related to H (Riesz transforms, maximal operators, Littlewood-Paley g-functions and variation operators).

math.CA↗