Titlebook: Analysis in Banach Spaces; Volume II: Probabili Tuomas Hyt?nen,Jan van Neerven,Lutz Weis Book 2017 Springer International Publishing AG 201

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Infinite-Impulse-Response-Systeme,tial tools in deeper manipulations of random sums arising in their applications to various domains of analysis. We discuss both the general operator-theoretic mechanisms of creating .-bounded families, and concrete sources and applications of .-boundedness in classical analysis. One section is dedic

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Random sums,ments throughout this volume. Here we concentrate on general properties of random sums that remain valid in arbitrary Banach spaces, while more specific results connected with the geometry of the underlying space are taken up in the following chapter. In the present chapter, we establish a range of

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-boundedness,tial tools in deeper manipulations of random sums arising in their applications to various domains of analysis. We discuss both the general operator-theoretic mechanisms of creating .-bounded families, and concrete sources and applications of .-boundedness in classical analysis. One section is dedic

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Square functions and radonifying operators,eas from classical Littlewood--Paley theory in . spaces to more general Banach spaces. The space of radonifying operators is shown to display several function-space-like properties, including H?lder-type duality, convergence and Fubini theorems. Pointwise multipliers of this space are characterised

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The ,-functional calculus,ctional calculus of sectorial and bi-sectorial operators in a Banach space. We begin with a general theory of the sectorial operators and a construction of the .-calculus, complemented by several examples. In two sections, we connect the .-calculus to .-boundedness on the one hand, and to the genera

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