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

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

Heat and Poisson semigroups for Fourier-Neumann expansions

Given $\alpha > -1$, consider the second order differential operator in $(0,\infty)$, $$L_\alpha f \equiv (x^2 \frac{d^2}{dx^2} + (2\alpha+3)x \frac{d}{dx} + x^2 + (\alpha+1)^2)(f),$$ which appears in the theory of Bessel functions. The purpose of this paper is to develop the corresponding harmonic analysis taking $L_\alpha$ as the analogue to the classical Laplacian. Namely we study the boundedness properties of the heat and Poisson semigroups. These boundedness properties allow us to obtain some convergence results that can be used to solve the Cauchy problem for the corresponding heat and Poisson equations.Comment: 16 page

LpL^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 Calder\'on) 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.Comment: 8 page

Stabilization of b-Glucuronidase by Immobilization in Magnetic-Silica Hybrid Supports

beta-Glucuronidases are a class of enzymes that catalyze the breakdown of complex carbohydrates. They have well documented biocatalytic applications in synthesis, therapeutics, and analytics that could benefit from enzyme immobilization and stabilization. In this work, we have explored a number of immobilization strategies for Patella vulgata beta-Glucuronidase that comprised a tailored combination of biomimetic silica (Si) and magnetic nanoparticles (MNPs). The individual effect of each material on the enzyme upon immobilization was first tested. Three different immobilization strategies for covalent attachment on MNPs and different three catalysts for the deposition of Si particles were tested. We produced nine different immobilized preparations and only two of them presented negligible activity. All the preparations were in the micro-sized range (from 1299 +/- 52 nm to 2101 +/- 67 nm of hydrodynamic diameter). Their values for polydispersity index varied around 0.3, indicating homogeneous populations of particles with low probability of agglomeration. Storage, thermal, and operational stability were superior for the enzyme immobilized in the composite material. At 80 degrees C different preparations with Si and MNPs retained 40% of their initial activity after 6 h of incubation whereas the soluble enzyme lost 90% of its initial activity within 11 min. Integration of MNPs provided the advantage of reusing the biocatalyst via magnetic separation up to six times with residual activity. The hybrid material produced herein demonstrated its versatility and robustness as a support for beta-Glucuronidases immobilization

γ-Radonifying operators and UMD-valued Littlewood–Paley–Stein functions in the Hermite setting on BMO and Hardy spaces

AbstractIn this paper we study Littlewood–Paley–Stein functions associated with the Poisson semigroup for the Hermite operator on functions with values in a UMD Banach space B. If we denote by H the Hilbert space L2((0,∞),dt/t), γ(H,B) represents the space of γ-radonifying operators from H into B. We prove that the Hermite square function defines bounded operators from BMOL(Rn,B) (respectively, HL1(Rn,B)) into BMOL(Rn,γ(H,B)) (respectively, HL1(Rn,γ(H,B))), where BMOL and HL1 denote BMO and Hardy spaces in the Hermite setting. Also, we obtain equivalent norms in BMOL(Rn,B) and HL1(Rn,B) by using Littlewood–Paley–Stein functions. As a consequence of our results, we establish new characterizations of the UMD Banach spaces