JournalszaaVol. 26, No. 3pp. 341–362

Metric and <em>ω*</em>-Differentiability of Pointwise Lipschitz Mappings

  • Jakub Duda

    Weizmann Institute of Science, Rehovot, Israel
Metric and <em>ω*</em>-Differentiability of Pointwise Lipschitz Mappings cover

Abstract

We study the metric and ww^*-differentiability of pointwise Lipschitz mappings. First, we prove several theorems about metric and ww^*-differentiability of pointwise Lipschitz mappings between \Rn\Rn and a Banach space XX (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,λ)(n,\lambda)-absolutely continuous functions with values in Banach spaces. In~the second part of this paper, we prove two theorems concerning metric and ww^*-differentiability of pointwise Lipschitz mappings f:XYf:X\mapsto Y where X,YX,Y are Banach spaces with XX being separable (resp.\ XX separable and Y=GY=G^* with GG separable).

Cite this article

Jakub Duda, Metric and <em>ω*</em>-Differentiability of Pointwise Lipschitz Mappings. Z. Anal. Anwend. 26 (2007), no. 3, pp. 341–362

DOI 10.4171/ZAA/1328