Iterated Littlewood-Paley functions and a multiplier theorem

Madych, W. R.

doi:10.1090/S0002-9939-1974-0355475-8

Iterated Littlewood-Paley functions and a multiplier theorem
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by W. R. Madych PDF

Proc. Amer. Math. Soc. 45 (1974), 325-331 Request permission

Abstract:

A sufficient condition for a bounded function to be a multiplier of Fourier transforms on ${L^p}({R^n}),1 < p < \infty$, is established. The classical case of Marcinkiewicz is properly included. The main tools used in obtaining this result are iterated variants of the classical LittlewoodPaley functions together with an ${L^p}$ estimate on certain maximal functions closely related to strong differentiability of multiple integrals.

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Note on the differentiability of multiple integrals

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