Norms on possibilities. II: More ccc ideals on .
We show a first nontrivial example of coarea formula for vector-valued Lipschitz maps defined on the three dimensional Heisenberg group. In this coarea formula, integration on level sets is performed with respect to the 2-dimensional spherical Hausdorff measure, built by the Carnot-Carathéodory distance. The standard jacobian is replaced by the so called horizontal jacobian, corresponding to the jacobian of the Pansu differential of the Lipschitz map. Joining previous results, we achieve all possible...
We introduced the notion of -boundedness of a filtered family of operators in the Musielak-Orlicz sequence space of multifunctions. This notion is used to get the convergence theorems for the families of -linear operators, -dist-sublinear operators and -dist-convex operators. Also, we prove that is complete.
We introduce the spaces , , and of multifunctions. We prove that the spaces and are complete. Also, we get some convergence theorems.