$H^1$-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis II

$H^1$-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis II

Year:    2016

Analysis in Theory and Applications, Vol. 32 (2016), Iss. 1 : pp. 38–51

Abstract

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

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2016.v32.n1.4

Analysis in Theory and Applications, Vol. 32 (2016), Iss. 1 : pp. 38–51

Published online:    2016-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    14

Keywords:    Jacobi analysis Jacobi hypergroup $g$ function area function real Hardy space.