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

Betancor, Jorge J.Castro, Alejandro J.Fariña, Juan C.Rodríguez-Mesa, L.2017-12-222017-12-222017-03-01Jorge J. Betancor, Alejandro J. Castro, Juan C. Fariña, L. Rodríguez-Mesa, Conical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spaces, In Journal of Mathematical Analysis and Applications, Volume 447, Issue 1, 2017, Pages 32-750022247Xhttps://www.sciencedirect.com/science/article/pii/S0022247X16305923http://nur.nu.edu.kz/handle/123456789/3012Abstract 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<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.enConical square functionsVector-valued harmonic analysisUMD Banach spacesBesselLaguerreSchrödingerConical square functions associated with Bessel, Laguerre and Schrödinger operators in UMD Banach spacesArticle© 2016 Elsevier Inc. All rights reserved.