Analyse fonctionnelle dans l’espace euclidien. (Functional analysis in Euclidean space). (French) Zbl 0627.46048

Bourdaud, Gérard

Publications Mathématiques de l’Université Paris VII, 23. Paris: U.E.R. de Mathématiques de Paris VII. 191 p. (1986).

The present book consists of seven chapters. In the first one the main definitions of the theory of distributions are given and in the second chapter the notion of interpolation of operators is introduced. The chapters three and four deal with multipliers and convolutors. The fifth chapter studies integral operators with singular kernels. Chapter six discusses \(L^ p\)-continuity of the pseudo-differential operators and the last chapter gives a characterization of bounded singular integral operators on the space \(L^ 2\).

Reviewer: L.Janos

MSC:

46F10	Operations with distributions and generalized functions
46-02	Research exposition (monographs, survey articles) pertaining to functional analysis
47Gxx	Integral, integro-differential, and pseudodifferential operators
47-02	Research exposition (monographs, survey articles) pertaining to operator theory
46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46M35	Abstract interpolation of topological vector spaces
47B38	Linear operators on function spaces (general)

Keywords:

distributions; interpolation of operators; multipliers; convolutors; integral operators with singular kernels; \(L^ p\)-continuity of the pseudo-differential operators; bounded singular integral operators