By Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis

ISBN-10: 3319485199

ISBN-13: 9783319485195

ISBN-10: 3319485202

ISBN-13: 9783319485201

The current quantity develops the idea of integration in Banach areas, martingales and UMD areas, and culminates in a remedy of the Hilbert remodel, Littlewood-Paley thought and the vector-valued Mihlin multiplier theorem.

Over the prior fifteen years, stimulated via regularity difficulties in evolution equations, there was large growth within the research of Banach space-valued features and procedures.

The contents of this broad and strong toolbox were regularly scattered round in study papers and lecture notes. amassing this different physique of fabric right into a unified and available presentation fills a niche within the present literature. The primary viewers that we've got in brain involves researchers who want and use research in Banach areas as a device for learning difficulties in partial differential equations, harmonic research, and stochastic research. Self-contained and delivering entire proofs, this paintings is available to graduate scholars and researchers with a history in useful research or comparable areas.

Show description

Read Online or Download Analysis in Banach Spaces : Volume I: Martingales and Littlewood-Paley Theory PDF

Best functional analysis books

Download PDF by John B Conway: A Course in Functional Analysis

This booklet is an introductory textual content in practical research. in contrast to many smooth remedies, it starts off with the actual and works its strategy to the extra normal. From the studies: "This ebook is a superb textual content for a primary graduate path in sensible research. .. .Many fascinating and demanding functions are integrated.

Read e-book online Current Topics in Pure and Computational Complex Analysis PDF

The booklet comprises thirteen articles, a few of that are survey articles and others study papers. Written by way of eminent mathematicians, those articles have been awarded on the foreign Workshop on complicated research and Its purposes held at Walchand university of Engineering, Sangli. the entire contributing authors are actively engaged in learn fields on the topic of the subject of the publication.

Read e-book online An Advanced Complex Analysis Problem Book: Topological PDF

This is often an routines publication before everything graduate point, whose objective is to demonstrate many of the connections among sensible research and the idea of capabilities of 1 variable. A key function is performed through the notions of confident yes kernel and of reproducing kernel Hilbert area. a few evidence from sensible research and topological vector areas are surveyed.

Additional info for Analysis in Banach Spaces : Volume I: Martingales and Littlewood-Paley Theory

Sample text

Suppose g is as stated in the proposition. Since g(s, ·) = F (s) in Lp (T ; X) for almost all s ∈ S, for almost all s ∈ S we have g(s, t) = f (s, t) for almost all t ∈ T . Hence, by Fubini’s theorem, g(s, t) = f (s, t) for (µ × ν)-almost all (s, t) ∈ S × T . 26. If ν is σ-finite, the result also holds for p = ∞. 29. We continue with a criterion for separability of Bochner spaces. We shall need the following terminology. 27. A measure space (S, A , µ) is called: (a) countably generated, if there exists a sequence (Sn )n 1 in A which generates A .

If f : S → L (X, Y ) and g : S → L (Y, Z) are strongly (µ-)measurable, then g ◦ f : S → L (X, Z) is strongly (µ-)measurable. Proof. Let x ∈ X be fixed. Since s → f (s)x is strongly (µ-)measurable, the preceding proposition shows that s → gf (s)x is strongly (µ-)measurable for all x ∈ X, so that g ◦ f is strongly (µ-)measurable. 2 Integration In this section we discuss the vector-valued extension of the Lebesgue integral, the so-called Bochner integral. At various places in this book we will also need its ‘weak’ companion, the Pettis integral.

Occasionally we will write, when F is a sub-σ-algebra of A , Lp (S, F ; X) for the Lp -space with respect to the measure space (S, F , µ|F ). It coincides with the closed linear subspace of Lp (S; X) consisting of all equivalence classes of functions with a representative that is strongly µ-measurable with respect to F . We write Lp (S, F ) := Lp (S, F ; K). 17. For a strongly µ-measurable function f : S → X the following assertions are equivalent: (1) f ∈ L∞ (S; X); (2) f, x∗ ∈ L∞ (S) for all x∗ ∈ X ∗ .

Download PDF sample

Analysis in Banach Spaces : Volume I: Martingales and Littlewood-Paley Theory by Tuomas Hytönen, Jan van Neerven, Mark Veraar, Lutz Weis

by Robert

Rated 4.68 of 5 – based on 42 votes