Erschienen in:

1988 | OriginalPaper | Buchkapitel

One Product of Distributions

verfasst von : Miloš Tomić

Erschienen in: Generalized Functions, Convergence Structures, and Their Applications

Verlag: Springer US

Enthalten in: Professional Book Archive

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In this paper we prove the inequality by which the Fourier transform of the product |x|r s(x) for s ∈ S(ℝ_n), x ∈ ℝ_n, r > 0, is estimated. The product $${\left| {\text{x}} \right|^{\text{r}}}\cdot\mathop f\limits^ \wedge$$ is also defined, where f is a real locally integrable function on ℝ_n and $$\mathop f\limits^ \wedge$$ it is the Fourier transforms and its proved that this product is a tempered distribution.

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