Zeitschrift für Analysis und ihre Anwendungen
Full-Text PDF (216 KB) | Abstract as PDF | Metadata | Table of Contents | ZAA summary
Published online: 2007-09-30
Metric and ω*-Differentiability of Pointwise Lipschitz MappingsJakub Duda (1) Weizmann Institute of Science, Rehovot, Israel
We study the metric and $w^*$-differentiability of pointwise Lipschitz mappings. First, we prove several theorems about metric and $w^*$-differentiability of pointwise Lipschitz mappings between $\Rn$ and a Banach space $X$ (which extend results due to Ambrosio, Kirchheim and others), then apply these to functions satisfying the spherical Rado--Reichelderfer condition, and to absolutely continuous functions of several variables with values in a Banach space. We also establish the area formula for pointwise Lipschitz functions, and for $(n,\lambda)$-absolutely continuous functions with values in Banach spaces. In~the second part of this paper, we prove two theorems concerning metric and $w^*$-differentiability of pointwise Lipschitz mappings $f:X\mapsto Y$ where $X,Y$ are Banach spaces with $X$ being separable (resp.\ $X$ separable and $Y=G^*$ with $G$ separable).
Keywords: Lipschitz mappings, pointwise Lipschitz mappings, metric differentiability, ω*-differentiability, absolutely continuous functions of several variables, area formula, Radon–Nikodým property, Aronszajn null sets
Duda Jakub: Metric and ω*-Differentiability of Pointwise Lipschitz Mappings. Z. Anal. Anwend. 26 (2007), 341-362. doi: 10.4171/ZAA/1328