Volume 32, Issue 1
H1-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 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.
  • Keywords

Jacobi analysis Jacobi hypergroup g function area function real Hardy space

  • AMS Subject Headings

22E30 43A30 43A80

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{ATA-32-38, author = {T. Kawazoe}, title = {H1-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 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.}, 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 - H1-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis II AU - T. Kawazoe 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 KW - Jacobi hypergroup KW - g function KW - area function KW - real Hardy space AB - 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.
T. Kawazoe. (1970). H1-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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