Scalar oscillatory integrals in smooth spaces of homogeneous type

• Philip T. Gressman ^[1]
  1. [1] University of Pennsylvania

     University of Pennsylvania

     City of Philadelphia, Estados Unidos

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 1, 2015, págs. 215-244
• Idioma: inglés
• DOI: 10.4171/RMI/831
• Texto completo no disponible (Saber más ...)
• Resumen

  • We consider a generalization of the notion of spaces of homogeneous type, inspired by recent work of Street (2011) on the multi-parameter Carnot–Carathéodory geometry, which endows such spaces with differential structure. The setting allows one to formulate estimates for scalar oscillatory integrals on these spaces which are uniform and respect the underlying geometry of both the space and the phase function. As a corollary we obtain a generalization of a theorem of Bruna, Nagel, and Wainger (1988) on the asymptotic behavior of scalar oscillatory integrals with smooth, convex phase of finite type.