## Tuomas

7 records found

1

## Authored

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.

@enThis chapter presents an in-depth study of several classes of vector-valued function spaces defined by smoothness conditions.

@enIn 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^{∞}-c
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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 ope ...

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 o
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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.

@enIn this chapter, we complement the discussion of three major themes of Fourier analysis that we have studied in the previous Volumes.

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