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Notes on integral transformations

Paweł Szeptycki — 1984

CONTENTS1. Introduction...............................................................................52. Spaces of measurable functions...............................................73. Proper domain of an integral transformation...........................144. Integral transformations in L⁰. Continuity and closibility...........175. Extensions by continuity. Compatibility problem.......................216. Compactness of integral transformations................................357. Miscellaneous...

Domains of integral operators

Iwo LabudaPaweł Szeptycki — 1994

Studia Mathematica

It is shown that the proper domains of integral operators have separating duals but in general they are not locally convex. Banach function spaces which can occur as proper domains are characterized. Some known and some new results are given, illustrating the usefulness of the notion of proper domain.

Theory of Bessel potentials. IV. Potentials on subcartesian spaces with singularities of polyhedral type

Nachman AronszajnPawel Szeptycki — 1975

Annales de l'institut Fourier

In the previous parts of the series on Bessel potentials the present part was announced as dealing with . The last notion is best defined in the more general framework of . In a subcartesian space X we define the local potentials of α : u P loc α ( X ) , if for any chart ( U , φ , R n ) of the structure of X , u γ - 1 can be extended from φ ( U ) to the whole of R n as potential in P loc α + ( n / 2 ) ( R n ) . This definition is not intrinsic. We obtain an intrinsic characterization of P loc α ( X ) when X is with , i.e. form some atlas of X the image of each chart is...

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