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

T. Kawazoe

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

Published online: 2016-01

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  • 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.

  • AMS Subject Headings

22E30, 43A30, 43A80

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-32-38, author = {}, title = {$H^1$-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis II}, journal = {Analysis in Theory and Applications}, year = {2016}, volume = {32}, number = {1}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2016.v32.n1.4}, url = {http://global-sci.org/intro/article_detail/ata/4653.html} }
TY - JOUR T1 - $H^1$-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis II JO - Analysis in Theory and Applications VL - 1 SP - 38 EP - 51 PY - 2016 DA - 2016/01 SN - 32 DO - http://doi.org/10.4208/ata.2016.v32.n1.4 UR - https://global-sci.org/intro/article_detail/ata/4653.html KW - Jacobi analysis, Jacobi hypergroup, $g$ function, area function, real Hardy space. AB -

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.

T. Kawazoe. (1970). $H^1$-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis II. Analysis in Theory and Applications. 32 (1). 38-51. doi:10.4208/ata.2016.v32.n1.4
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