JournalsrmiVol. 31, No. 1pp. 215–244

Scalar oscillatory integrals in smooth spaces of homogeneous type

  • Philip T. Gressman

    University of Pennsylvania, Philadelphia, USA
Scalar oscillatory integrals in smooth spaces of homogeneous type cover
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Abstract

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.

Cite this article

Philip T. Gressman, Scalar oscillatory integrals in smooth spaces of homogeneous type. Rev. Mat. Iberoam. 31 (2015), no. 1, pp. 215–244

DOI 10.4171/RMI/831