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Harmonic analysis is a generalisation of Fourier analysis that studies the properties of functions. Check out this tag for abstract harmonic analysis (on abelian locally compact groups), or Euclidean harmonic analysis (eg, Littlewood-Paley theory, singular integrals). It also covers harmonic analysis on tube domains, as well as the study of eigenvalues and eigenvectors of the Laplacian on domains, manifolds and graphs.

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Marcinkiewicz-Mihlin-Hormander Fourier multiplier theorem

I'm trying to understand the hypothesis of the Marcinkiewicz-Mihlin-Hörmander multiplier theorem. See for instance Theorem A in this paper of Elias Stein. Theorem A: Assume that $m: (0, \infty)\to \m …
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