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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.
6
votes
How was Claim 5 in "A non-linear generalisation of the Loomis–Whitney inequality and applica...
An instance of this idea of killing an unwanted factor in an inequality by considering an inequality for $k$-th powers and then taking the limit as $k\to\infty$ appears in the proof of the Kraft-McMil …