Applications of the Littlewood-Paley Theorem
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In this chapter, we show how the Littlewood-Paley theorem for ℤ can be used to construct (i) examples of sets which are ⋀(p) for every p; and (ii) an example of a multiplier of L p which is in a certain sense “singular”. The results are due to Meyer  and Figà-Talamanca and Gaudry  respectively.
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