R-boundedness and operator-valued Fourier multiplier theorems

Tobias Nau

Chapter 3 in Lp-Theory of Cylindrical Boundary Value Problems, 2012, pp 25-39 from Springer

Abstract: Abstract In this chapter we present results on operator-valued Fourier multipliers both in the context of Fourier transform and Fourier series. They employ the concept of R-boundedness which we introduce next. With R-boundedness at hand, conditions can be deduced which make sure that a function defines a Fourier multiplier. Besides that, R-boundedness is as well involved in necessary conditions for Fourier multipliers.

Keywords: Banach Space; Fourier Series; Trigonometric Polynomial; Fourier Multiplier; Contraction Principle (search for similar items in EconPapers)
Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-8348-2505-6_3

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DOI: 10.1007/978-3-8348-2505-6_3

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