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The first author was supported by a contract of the Programa de Ayudas de Investigacion y Desarrollo (PAID-01-21), Universitat Politecnica de Valencia. This research was funded by the Agencia Estatal de Investigacion grant number PID2022-138342NB-I00. The research was funded by the European Union's Horizon Europe research and innovation program under the Grant Agreement No. 101059609 (Re-Livestock).

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Eccentric p-Summing Lipschitz Operators and Integral Inequalities on Metric Spaces and Graphs

Publicat a:Axioms: Mathematical Logic And Mathematical Physics. 13 (11): 760- - 2024-11-01 13(11), DOI: 10.3390/axioms13110760

Autors: Arnau, Roger; Perez, Enrique A Sanchez; Sanjuan, Sergi

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The extension of the concept of p-summability for linear operators to the context of Lipschitz operators on metric spaces has been extensively studied in recent years. This research primarily uses the linearization of the metric space M afforded by the associated Arens-Eells space, along with the duality between M and the metric dual space M# defined by the real-valued Lipschitz functions on M. However, alternative approaches to measuring distances between sequences of elements of metric spaces (essentially involved in the definition of p-summability) exist. One approach involves considering specific subsets of the unit ball of M# for computing the distances between sequences, such as the real Lipschitz functions derived from evaluating the difference in the values of the metric from two points to a fixed point. We introduce new notions of summability for Lipschitz operators involving such functions, which are characterized by integral dominations for those operators. To show the applicability of our results, in the last part of this paper, we use the theoretical tools obtained in the first part to analyze metric graphs. In particular, we show new results on the behavior of numerical indices defined on these graphs satisfying certain conditions of summability and symmetry.

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