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Fourier Transform and Compactness in (Lq, lp)a and Mp,a Spaces

Commun. Math. Anal.
Volume 11, Number 2 (2011), 139 - 153

Fourier Transform and Compactness in (Lq, lp)a and Mp,a Spaces

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Abstract

The spaces (Lq,lp)α and Mp,α are closely related to classical problems in Harmonic Analysis: properties of multiplier and Fourier multiplier from a Lebesgue space to another, finite (1,p)-energy measures. We characterize the Fourier transforms of their elements and establish criteria of compactness in these spaces.