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BMO-scale of distribution on n

René Erlín Castillo, Julio C. Ramos Fernández (2008)

Czechoslovak Mathematical Journal

Let S ' be the class of tempered distributions. For f S ' we denote by J - α f the Bessel potential of f of order α . We prove that if J - α f B M O , then for any λ ( 0 , 1 ) , J - α ( f ) λ B M O , where ( f ) λ = λ - n f ( φ ( λ - 1 · ) ) , φ S . Also, we give necessary and sufficient conditions in order that the Bessel potential of a tempered distribution of order α > 0 belongs to the V M O space.

Boehmians of type S and their Fourier transforms

R. Bhuvaneswari, V. Karunakaran (2010)

Annales UMCS, Mathematica

Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.

Boolean Rings that are Baire Spaces

Haydon, R. (2001)

Serdica Mathematical Journal

∗ The present article was originally submitted for the second volume of Murcia Seminar on Functional Analysis (1989). Unfortunately it has been not possible to continue with Murcia Seminar publication anymore. For historical reasons the present vesion correspond with the original one.Weak completeness properties of Boolean rings are related to the property of being a Baire space (when suitably topologised) and to renorming properties of the Banach spaces of continuous functions on the corresponding...

Bootstrapping Kirszbraun's extension theorem

Eva Kopecká (2012)

Fundamenta Mathematicae

We show how Kirszbraun's theorem on extending Lipschitz mappings in Hilbert space implies its own generalization. There is a continuous extension operator preserving the Lipschitz constant of every mapping.

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