Abstract

CARDONA, DUVÁN. Pseudo-differential operators defined on Borel measures. Integración - UIS [online]. 2013, vol.31, n.1, pp.25-42. ISSN 0120-419X.

In this paper we introduce a type of pseudo-differential operators defined on Borel measures. Classically the definition of pseudo-differential operators extends the tempered distributions space, but in its representation does not intervene the Fourier analysis in measures spaces. The main objective is to define such operators at a different angle and establish boundedness results on suitable normed spaces, in addition to providing a connection with the pseudo-differential operators theory with symbols in the classes defined on ℝⁿ and the torus Tⁿ.

Keywords : Pseudo-differential operators; Borel measures; Radon-Nikodým Theorem; Boundedness and compactness of operators; Distributions; Elliptic operators.

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