Optimal quasi-metrics in a given pointwise equivalence class do not always exist

• Autores: Dan Brigham, Marius Mitrea
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 59, Nº 2, 2015, págs. 479-509
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this paper we provide an answer to a question found in [3], namely when given a quasi-metric p, if one examines all quasi-metrics which are pointwise equivalent to p, does there exist one which is most like an ultrametric (or, equivalently, exhibits an optimal amount of Hölder regularity)? The answer, in general, is negative, which we demonstrate by constructing a suitable Rolewicz-Orlicz space.