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A characterization of a two-weight inequality for discrete two-dimensional Hardy operators.

Rakotondratsimba, Y. (1999)

Zeitschrift für Analysis und ihre Anwendungen

A characterization of $C^{1, 1}$ functions via lower directional derivatives

Dušan Bednařík, Karel Pastor (2009)

Mathematica Bohemica

The notion of $\tilde{ℓ}$ -stability is defined using the lower Dini directional derivatives and was introduced by the authors in their previous papers. In this paper we prove that the class of $\tilde{ℓ}$ -stable functions coincides with the class of C $^{1, 1}$ functions. This also solves the question posed by the authors in SIAM J. Control Optim. 45 (1) (2006), pp. 383–387.

A characterization of chaotic functions with entropy zero via their maximal scrambled sets

Francisco Balibrea, Víctor Jiménez López (1995)

Mathematica Bohemica

In this note we characterize chaotic functions (in the sense of Li and Yorke) with topological entropy zero in terms of the structure of their maximal scrambled sets. In the interim a description of all maximal scrambled sets of these functions is also found.

A characterization of midconvex set-valued functions

Kazimierz Nikodem (1989)

Acta Universitatis Carolinae. Mathematica et Physica

A characterization of monomial functions.

Attila Gilányi (1997)

Aequationes mathematicae

A characterization of sets in $ℝ^{2}$ with DC distance function

Dušan Pokorný, Luděk Zajíček (2022)

Czechoslovak Mathematical Journal

We give a complete characterization of closed sets $F \subset ℝ^{2}$ whose distance function $d_{F} : = dist (\cdot, F)$ is DC (i.e., is the difference of two convex functions on $ℝ^{2}$ ). Using this characterization, a number of properties of such sets is proved.

A characterization of Sobolev spaces via local derivatives

David Swanson (2010)

Colloquium Mathematicae

Let 1 ≤ p < ∞, k ≥ 1, and let Ω ⊂ ℝⁿ be an arbitrary open set. We prove a converse of the Calderón-Zygmund theorem that a function $f \in W^{k, p} (Ω)$ possesses an $L^{p}$ derivative of order k at almost every point x ∈ Ω and obtain a characterization of the space $W^{k, p} (Ω)$ . Our method is based on distributional arguments and a pointwise inequality due to Bojarski and Hajłasz.

A characterization of some classes of functions F of the form F(x, y) = g(...f(x) + ßf(y) + ...) or F(x, y) = ...(h(x) + k(y)).

Luigi Paganoni, Daniela Rusconi (1983)

Aequationes mathematicae

A characterization of space-filling curves.

Gaspar Mora, Juan A. Mira (2002)

RACSAM

En este artículo revisamos un famoso teorema, descubierto por H. Steinhaus en 1936, en el que se da una condición suficiente que permite obtener las funciones coordenadas de una curva que llena el cuadrado unidad. Ponemos de manifiesto que el recíproco de este teorema no se cumple para la curva de Lebesgue. Aquí proponemos un teorema de caracterización de curvas que llenan el espacio, basado en una condición de llenado. Asimismo, damos una caracterización constructiva de esta condición de llenado...