MR2789279 Aziz, Wadie; Leiva, Hugo; Merentes, Nelson; Rzepka, Beata A representation theorem for φ-bounded variation of functions in the sense of Riesz. Comment. Math. 50 (2010), no. 2, 109–120. (Reviewer: Pasquale Vetro)

Risultato della ricerca: Review articlepeer review

Abstract

The authors consider the class $V_\varphi^R (I^b_a)$ of functions $f:I^b_a =[a_1,b_1]\times [a_2,b_2]\subset \mathbb{R}^2 \to\mathbb{R}$ with bounded $\varphi$-total variation in the sense of Riesz, where $\varphi: [0,+ \infty) \to [0,+ \infty)$ is nondecreasing and continuous with $\varphi(0)=0$ and $\varphi(t) \to+\infty$ as $t \to +\infty$. If we assume that $\varphi$ is also such that $\lim_{t \to +\infty}\frac{\varphi(t)}{t}=+\infty$, then we obtain the main result. Precisely, the authors give a characterization of function of two variables defined on a rectangle $I^b_a$ belonging to $V_\varphi^R (I^b_a)$. Clearly, thisresult is a generalization of the Riesz Lemma.
Lingua originaleEnglish
Numero di pagine0
RivistaMATHEMATICAL REVIEWS
Volume2012
Stato di pubblicazionePublished - 2012

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