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Special functions, orthogonal polynomials, harmonic analysis, ordinary differential equations (ODE's), differential relations, calculus of variations, approximations, expansions, asymptotics.

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$L^p$-norm of Fourier series in terms of coefficients, $p \neq 2$

The answer is "not really, except in the sense that Carlo Beenaker has mentioned". I suggest you look at the discussion of the Hausdorff–Young inequality in Chapter IV Section 2 of Katznelson's Intro …
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