R-boundedness and operator-valued Fourier multiplier theorems
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.
KeywordsBanach Space Fourier Series Trigonometric Polynomial Fourier Multiplier Contraction Principle
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