LW
Lutz Weis
32 records found
1
In this chapter, we complement the discussion of three major themes of Fourier analysis that we have studied in the previous Volumes.@en
In this chapter we address a couple of topics in the theory of H∞-calculus centering around the question what can be said about an operator of the form A+B when A and B have certain “good” properties such as being (R-)sectorial or admitting a bounded H∞-calc
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As we have seen in the preceding sections, in the context of inhomogeneous linear evolution equations, maximal regularity enables one to set up an isomorphism between the space of data (initial value and inhomogeneity) and the solution space.@en
In this chapter we address two strongly interwoven topics: How to verify the boundedness of the H∞-calculus of an operator and how to represent and estimate its fractional powers. For concrete operators such as the Laplace operator or elliptic partial differential oper
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Analysis in Banach Spaces
Volume III. Harmonic Analysis and Spectral Theory
This third volume of Analysis in Banach Spaces offers a systematic treatment of Banach space-valued singular integrals, Fourier transforms, and function spaces. It further develops and ramifies the theory of functional calculus from Volume II and describes applications of these n
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Before addressing this question for the Calderón{Zygmund type operators of the kind studied in Chapter 11, we investigate a number of related objects in a simpler dyadic model. Besides serving as an introduction to some of the key techniques, it turns out that these dyadic operat
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We present a general method to extend results on Hilbert space operators to the Banach space setting by representing certain sets of Banach space operators Γ on a Hilbert space. Our assumption on Γ is expressed in terms of α-boundedness for a Euclidean structure α on the underlyi
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This chapter presents an in-depth study of several classes of vector-valued function spaces defined by smoothness conditions.@en
The mapping properties of T will of course heavily depend on the assumptions made on the kernel K that we will discuss in more detail in this chapter.@en
Analysis in Banach Spaces
Volume II. Probabilistic Methods and Operator Theory
This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the th
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Analysis in Banach Spaces
Volume I: Martingales and Littlewood-Paley Theory
The present volume develops the theory of integration in Banach spaces, martingales and UMD spaces, and culminates in a treatment of the Hilbert transform, Littlewood-Paley theory and the vector-valued Mihlin multiplier theorem.
Over the past fifteen years, motivated by regul ...
Over the past fifteen years, motivated by regul ...
It is well-known that in Banach spaces with finite cotype, the R-bounded and γ-bounded families of operators coincide. If in addition X is a Banach lattice, then these notions can be expressed as square function estimates. It is also clear that R-boundedness implies γ-boundednes
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The R
-boundedness of certain families of vector-valued stochastic convolution operators with scalar-valued square integrable kernels is the key ingredient in the recent proof of stochastic maximal L p
-regularity, 2<p<∞
, for certain classes of sectorial operators a
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