Volume 32, Issue 1
H1-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis II

T. Kawazoe

10.4208/ata.2016.v32.n1.4

Anal. Theory Appl., 32 (2016), pp. 38-51

Preview Full PDF BiBTex 236 484
  • Abstract

Let $({\Bbb R}_+,*,\Delta)$ be the Jacobi hypergroup.We introduce analogues of the Littlewood-Paley $g$ function andthe Lusin area function for the Jacobi hypergroupand consider their $(H^1, L^1)$ boundedness.Although the $g$ operator for $({\Bbb R}_+,*,\Delta)$ possesses betterproperty than the classical $g$ operator, the Lusin area operator hasan obstacle arisen from a second convolution. Hence,in order to obtain the $(H^1, L^1)$ estimate forthe Lusin area operator, a slight modification in its form is required.

  • History

Published online: 2016-01

  • AMS Subject Headings

22E30, 43A30, 43A80

  • Cited by