Derivatives of Fourier series and integrals

Richard Wheeden

Displaying similar documents to “Derivatives of Fourier series and integrals”

Singular integrals and periodic functions

A. Calderón, Antoni Zygmund (1954)

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Note on the class LlogL

E. Stein (1969)

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Mean periodic functions on phase space and the Pompeiu problem with a twist

Sundaram Thangavelu (1995)

Annales de l'institut Fourier

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We show that when $f$ is a mean periodic function of tempered growth on the reduced Heisenberg group then the closed translation and rotation invariant subspace generated by $f$ contains an elementary spherical function. Using a Paley-Wiener theorem for the Fourier-Weyl transform we formulate a conjecture for arbitrary mean periodic functions.

Mean-periodic functions.

Berenstein, Carlos A., Taylor, B.A. (1980)

International Journal of Mathematics and Mathematical Sciences

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Periodic solutions of degenerate differential equations in vector-valued function spaces

Carlos Lizama, Rodrigo Ponce (2011)

Studia Mathematica

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Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multiplier theorems, we obtain necessary and sufficient conditions for the existence and uniqueness of periodic solutions to the equation d/dt(Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our results are obtained in the scales of periodic Besov and periodic Lebesgue vector-valued spaces. ...