2023/08/07 by M. G. Cabrera-Padilla, Cabrera-Padilla, M. G., A. Jiménez-Vargas +3
Mathematics · Biochemistry, Genetics and Molecular Biology · #Homotopy and Cohomology in Algebraic Topology #Advanced Topics in Algebra #Connective tissue disorders research
paper · pdf · doi:10.48550/arxiv.2308.03491
The notion of p-summing Bloch mapping from the complex unit open disc \mathbbD into a complex Banach space X is introduced for any 1≤ p≤∞. It is shown that the linear space of such mappings, equipped with a natural seminorm π^\mathbbBp, is Möbius-invariant. Moreover, its subspace consisting of all those mappings which preserve the zero is an injective Banach ideal of normalized Bloch mappings. Bloch versions of the Pietsch's domination/factorization Theorem and the Maurey's extrapolation Theorem are presented. We also introduce the spaces of X-valued Bloch molecules on \mathbbD and identify the spaces of normalized p-summing Bloch mappings from \mathbbD into X^* under the norm π^\mathbbBp with the duals of such spaces of molecules under the Bloch version of the p-Chevet--Saphar tensor norms dp.