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

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• 作者：Jorge J. Betancor^a ; ^{jbetanco@ull.es" class="auth_mail" title="E-mail the corresponding author} ; Alejandro J. Castro^b ; ^{alejandro.castilla@nu.edu.kz" class="auth_mail" title="E-mail the corresponding author} ; Juan C. Fariñ ; a^a ; ^{jcfarina@ull.es" class="auth_mail" title="E-mail the corresponding author} ; L. Rodr&iacute ; guez-Mesa^a ; ^{lrguez@ull.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Conical square functions ; Vector-valued harmonic analysis ; UMD Banach spaces ; Bessel ; Laguerre ; Schrö ; dinger
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：447
• 期：1
• 页码：32-75
• 全文大小：707 K

文摘

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)$L^p((0,\infty ),\mathbb{B})$ and L^p(Rⁿ,B)$L^p({\mathbb{R}}^n,\mathbb{B})$, 1<p<∞$1<p<\infty$, in terms of our square functions, provided that B$\mathbb{B}$ is a UMD Banach space. Our results can be seen as Banach valued versions of known scalar results for square functions.