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Let $S^{'}$ be the class of tempered distributions. For $f \in S^{'}$ we denote by $J^{- α} f$ the Bessel potential of $f$ of order $α$ . We prove that if $J^{- α} f \in B M O$ , then for any $λ \in (0, 1)$ , $J^{- α} {(f)}_{λ} \in B M O$ , where ${(f)}_{λ} = λ^{- n} f (φ (λ^{- 1} \cdot))$ , $φ \in S$ . 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.

Calculation of the Bidual for Some Function Spaces. Integrable Distributions.

Jürgen Voigt, Peter Dierolf (1980)

Mathematische Annalen

Characterization of Convolution Operators on Spaces of C-Functions Admitting a Continuous Linear Right Inverse.

Dietmar Vogt, Reinhold Meise (1987/1988)

Mathematische Annalen

Characterization of regular tempered distributions

Zofia Szmydt (1983)

Annales Polonici Mathematici

Characterization of some Subspaces of (D') by S-asymptotic

Bogoljub Stanković (1987)

Publications de l'Institut Mathématique

Characterization of the Colombeau product of distributions

Jiří Jelínek (1986)

Commentationes Mathematicae Universitatis Carolinae

Characterization of the $ω$ hypoelliptic convolution operators on ultradistributions.

Bonet, J., Fernández, C., Meise, R. (2000)

Annales Academiae Scientiarum Fennicae. Mathematica

Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives

Paweł Domański (2004)

Banach Center Publications

This paper is an extended version of an invited talk presented during the Orlicz Centenary Conference (Poznań, 2003). It contains a brief survey of applications to classical problems of analysis of the theory of the so-called PLS-spaces (in particular, spaces of distributions and real analytic functions). Sequential representations of the spaces and the theory of the functor Proj¹ are applied to questions like solvability of linear partial differential equations, existence of a solution depending...

Colombeau product of currents

Jiří Jelínek (2005)

Commentationes Mathematicae Universitatis Carolinae

Colombeau product of de Rham's currents coincides with generalized Itano one. Sufficient conditions are found under which it is diffeomorphism invariant.

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Approximationseigenschaft, Lifting und Kohomologie bei lokalkonvexen Produktgarben.

Automatic Continuity of Generalized Local Linear Operators.

Automatische Stetigkeitseigenschaften einiger Klassen linearer Operatoren.

Banach Spaces Related to Integrable Group Representations and Their Atomic Decompositions. Part II.

Bases in Spaces of Ultradifferentiable Functions with Compact Support.

Bieberbach functions and periodic distributions.

BMO-scale of distribution on $ℝ^{n}$