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On the characterization of Hardy-Besov spaces on the dyadic group and its applications

Jun Tateoka (1994)

Studia Mathematica

C. Watari [12] obtained a simple characterization of Lipschitz classes $L i p^{(p)} α (W) (1 \geq p \geq \infty, α > 0)$ on the dyadic group using the $L^{p}$ -modulus of continuity and the best approximation by Walsh polynomials. Onneweer and Weiyi [4] characterized homogeneous Besov spaces $B_{p, q}^{α}$ on locally compact Vilenkin groups, but there are still some gaps to be filled up. Our purpose is to give the characterization of Besov spaces $B_{p, q}^{α}$ by oscillations, atoms and others on the dyadic groups. As applications, we show a strong capacity inequality of the...

On the characterization of quasiarithmetic means with weight function.

Zsolt Páles (1987)

Aequationes mathematicae

On the Class Gamma and Related Classes of Functions

Edward Omey (2013)

Publications de l'Institut Mathématique

On the Classes of Rapidly Varying Functions

Slavko Simić (2003)

Publications de l'Institut Mathématique

On the closure of Baire classes under transfinite convergences

Tamás Mátrai (2004)

Fundamenta Mathematicae

Let X be a Polish space and Y be a separable metric space. For a fixed ξ < ω₁, consider a family $f_{α} : X \to Y (α < ω ₁)$ of Baire-ξ functions. Answering a question of Tomasz Natkaniec, we show that if for a function f: X → Y, the set $α < ω ₁ : f_{α} (x) \neq f (x)$ is finite for every x ∈ X, then f itself is necessarily Baire-ξ. The proof is based on a characterization of $Σ ⁰_{η}$ sets which can be interesting in its own right.

On the closure of the Lizorkin space in spaces of Beppo Levi type

Takahide Kurokawa (2002)

Studia Mathematica

The purpose of this paper is to give a characterization of the closure of the Lizorkin space in spaces of Beppo Levi type. As preparations for the proof, we establish the invariance of the Lizorkin space, and give local integral representations for smooth functions.