an:06136676
Zbl 1276.28028
Botelho, Geraldo; Pellegrino, Daniel; Rueda, Pilar; Santos, Joedson; Seoane-Sep??lveda, Juan Benigno
When is the Haar measure a Pietsch measure for nonlinear mappings?
EN
Stud. Math. 213, No. 3, 275-287 (2012).
00314877
2012
j
28C10 47B10
Haar measure; Pietsch measure; nonlinear mapping
Authors' abstract: ``We show that, as in the linear case, the normalized Haar measure on a compact topological group \(G\) is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of \(C(G)\). We also show that our result applies to several well-studied classes of nonlinear summing mappings. In the final section, some problems are proposed.''
One of the open problems reads as follows.
Let \(F\) be a closed translation invariant subspace of \(C(G)\), let \(X\) be a metric space and \(f: F\to X\) be a translation invariant Lipschitz \(p\)-summing mapping. Is the Haar measure a Pietsch measure for \(f\)?
Joe Howard (Portales)