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

Alejandro J. Castro; Jorge J. Betancor; Juan Carlos Fariña; Lourdes Rodríguez-Mesa

doi:10.1016/j.jmaa.2016.10.006

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

Alejandro J. Castro, Jorge J. Betancor, Juan Carlos Fariña, Lourdes Rodríguez-Mesa

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

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 [36], in order to define our conical square functions, we use γ-radonifying operators. We obtain new equivalent norms in the Lebesgue–Bochner spaces L^p((0,∞),B) and L^p(Rⁿ,B), 1<p<∞, in terms of our square functions, provided that B is a UMD Banach space. Our results can be seen as Banach valued versions of known scalar results for square functions.

Original language	English
Pages (from-to)	32-75
Number of pages	44
Journal	Journal of Mathematical Analysis and Applications
Volume	447
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2016.10.006
Publication status	Published - Mar 1 2017

Keywords

Bessel
Conical square functions
Laguerre
Schrödinger
UMD Banach spaces
Vector-valued harmonic analysis

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2016.10.006

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title = "Conical square functions associated with Bessel, Laguerre and Schr{\"o}dinger operators in UMD Banach spaces",

abstract = "In this paper we consider conical square functions in the Bessel, Laguerre and Schr{\"o}dinger settings where the functions take values in UMD Banach spaces. Following a recent paper of Hyt{\"o}nen, van Neerven and Portal [36], in order to define our conical square functions, we use γ-radonifying operators. We obtain new equivalent norms in the Lebesgue–Bochner spaces Lp((0,∞),B) and Lp(Rn,B), 1",

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author = "Castro, {Alejandro J.} and Betancor, {Jorge J.} and Fari{\~n}a, {Juan Carlos} and Lourdes Rodr{\'i}guez-Mesa",

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AU - Betancor, Jorge J.

AU - Fariña, Juan Carlos

AU - Rodríguez-Mesa, Lourdes

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AB - 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 [36], in order to define our conical square functions, we use γ-radonifying operators. We obtain new equivalent norms in the Lebesgue–Bochner spaces Lp((0,∞),B) and Lp(Rn,B), 1

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KW - Conical square functions

KW - Laguerre

KW - Schrödinger

KW - UMD Banach spaces

KW - Vector-valued harmonic analysis

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