Almost Lipschitz-continuous wavelets in metric spaces via a new randomization of dyadic cubes

• Autores: Tuomas P. Hytönen, Olli Tapiola
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 185, Nº 1, 2014, págs. 12-30
• Idioma: inglés
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• Resumen

  • In any quasi-metric space of homogeneous type, Auscher and Hyt¨onen recently gave a construction of orthonormal wavelets with H¨older-continuity exponent ç > 0. However, even in a metric space, their exponent is in general quite small. In this paper, we show that the H¨older-exponent can be taken arbitrarily close to 1 in a metric space. We do so by revisiting and improving the underlying construction of random dyadic cubes, which also has other applications.