Abstract
AbstractIn 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.KeywordsBanach SpaceFourier SeriesTrigonometric PolynomialFourier MultiplierContraction PrincipleThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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