Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces

Abstract

In this paper we consider conical square functions in the Bessel, Laguerre and Schrödinger settings where the functions take values in UMD Banach spaces. Following a recent paper of Hytönen, van Neerven and Portal, in order to define our conical square functions, we use $\gamma$-radonifying operators. We obtain new equivalent norms in the Lebesgue-Bochner spaces $L^p((0,\infty ),\mathbb{B})$ and $L^p({\mathbb{R}}^n,\mathbb{B})$, $1<p<\infty$, in terms of our square functions, provided that $\mathbb{B}$ is a UMD Banach space. Our results can be seen as Banach valued versions of known scalar results for square functions.

References in corpus (5)

• Stochastic integration in UMD Banach spaces
• Conical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi
• The $H^{\infty }$-Functional Calculus and Square Function Estimates
• On Harmonic Analysis Operators in Laguerre-Dunkl and Laguerre-Symmetrized Settings
• On vector-valued tent spaces and Hardy spaces associated with non-negative self-adjoint operators

Cited by in corpus (1)

• Lusin area integrals related to Jacobi expansions