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. Fari&ntilde ; 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 ; Schr&ouml ; 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 Schr&ouml;dinger settings where the functions take values in UMD Banach spaces. Following a recent paper of Hyt&ouml;nen, van Neerven and Portal [36], in order to define our conical square functions, we use <em>γ  em>-radonifying operators. We obtain new equivalent norms in the Lebesgue–Bochner spaces ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305923&_mathId=si1.gif&_user=111111111&_pii=S0022247X16305923&_rdoc=1&_issn=0022247X&md5=78048556e6010c0c9ce14e0190f66b8a" title="Click to view the MathML source">L^p((0,∞),B)er hidden">e"> and ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305923&_mathId=si2.gif&_user=111111111&_pii=S0022247X16305923&_rdoc=1&_issn=0022247X&md5=e7cb7d8ef0fbdc068f3f46fdc7eae96b" title="Click to view the MathML source">L^p(Rⁿ,B)er hidden">e">, ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305923&_mathId=si22.gif&_user=111111111&_pii=S0022247X16305923&_rdoc=1&_issn=0022247X&md5=11d4508e796370f7c892b12163739bd3" title="Click to view the MathML source">1<p<∞er hidden">e">, in terms of our square functions, provided that ext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16305923&_mathId=si4.gif&_user=111111111&_pii=S0022247X16305923&_rdoc=1&_issn=0022247X&md5=59459551365f1d02c5b08a4436a15270" title="Click to view the MathML source">Ber hidden">e"> is a UMD Banach space. Our results can be seen as Banach valued versions of known scalar results for square functions.