UMD-valued square functions associated with Bessel operators in Hardy and BMO spaces

We consider Banach valued Hardy and BMO spaces in the Bessel setting. Square functions associated with Poisson semigroups for Bessel operators are defined by using fractional derivatives. If B is a UMD Banach space we obtain for B-valued Hardy and BMO spaces equivalent norms involving $\gamma$-radonifying operators and square functions. We also establish characterizations of UMD Banach spaces by using Hardy and BMO-boundedness properties of g-functions associated to Bessel-Poisson semigroup

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

Area Littlewood-Paley functions associated with Hermite and Laguerre operators

In this paper we study Lp-boundedness properties for area Littlewood-Paley functions associated with heat semigroups for Hermite and Laguerre operator

UMD Banach spaces and square functions associated with heat semigroups for Schr\"odinger and Laguerre operators

In this paper we define square functions (also called Littlewood-Paley-Stein functions) associated with heat semigroups for Schr\"odinger 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 \gamma-radonifying operators. We also prove that these L^p-boundedness properties of the square functions actually characterize the Banach spaces having the UMD property

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