An endpoint estimate of the kunze-stein phenomenon on su(n,m)

Takeshi Kawazoe

Research output: Contribution to journalArticlepeer-review

Abstract

The endpoint estimates for the Kunze-Stein phenomenon associated with real rank one semisimple Lie groups and the Jacobi hypergroup were obtained by A. Ionescu and J. Liu respectively. Recently, a modified endpoint estimate was also proved for complex semisimple Lie groups by J. Liu and the author. Hence the original estimate seems not to be valid for general semisimple Lie groups with higher rank. We treat the case of SU(n,m) and obtain a modified estimate similarly to the complex case. The process using the Abel transform makes it clear why the original endpoint estimate might not be valid for general semisimple Lie groups.

Original languageEnglish
Pages (from-to)645-657
Number of pages13
JournalPacific Journal of Mathematics
Volume302
Issue number2
DOIs
Publication statusPublished - 2019 Jan 1

Keywords

  • Abel transform
  • Fourier multiplier
  • Kunze-Stein phenomenon
  • Lorentz space
  • Semisimple Lie group

ASJC Scopus subject areas

  • Mathematics(all)

Fingerprint Dive into the research topics of 'An endpoint estimate of the kunze-stein phenomenon on su(n,m)'. Together they form a unique fingerprint.

Cite this