The circular maximal operator on Heisenberg radial functions

• Autores: David Beltrán, Shaoming Guo, Jonathan Hickman, Andreas Seeger
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 23, Nº 2, 2022, págs. 501-568
• Idioma: inglés
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• Resumen

  • Lebesgue space estimates are obtained for the circular maximal function on the Heisenberg group H1 restricted to a class of Heisenberg radial functions. Under this assumption, the problem reduces to studying a maximal operator on the Euclidean plane. This operator has a number of interesting features: it is associated to a non-smooth curve distribution and, furthermore, fails both the usual rotational curvature and cinematic curvature conditions.