Using characteristic functions of polyhedra, we construct radial p-multipliers which are continuous over but not continuously differentiable through and give a p-multiplier criterion for homogeneous functions over . We also exhibit fractal p-multipliers over the real line.
On étudie un analogue à plusieurs variables réelles de la théorie de Riemann des séries trigonométriques vue sous l’angle des pseudofonctions, en utilisant le laplacien intégral et la fonction de Riemann qui découle de ce choix.
Using Bochner-Riesz means we get a multidimensional sampling theorem for band-limited functions with polynomial growth, that is, for functions which are the Fourier transform of compactly supported distributions.
Given a distribution on the sphere we define, in analogy to the work of Łojasiewicz, the value of at a point of the sphere and we show that if has the value at , then the Fourier-Laplace series of at is Abel-summable to .
We show that the Fourier-Laplace series of a distribution on the real, complex or quarternionic projective space is uniformly Cesàro-summable to zero on a neighbourhood of a point if and only if this point does not belong to the support of the distribution.
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