Hardy-Littlewood type inequalities for Laguerre series
Let {cj} be a null sequence of bounded variation. We give appreciate smoothness and growth conditions on {cj} to obtain the pointwise convergence as well as Lr-convergence of Laguerre series ∑cj𝔏ja. Then, we prove a Hardy-Littlewood type inequality ∫0∞|f(t)|rdt≤C∑j=0∞|cj|rj¯1−r/2 for certain r≤1, wh...
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| Format: | Article |
| Language: | English |
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Wiley
2002-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171202108234 |
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| _version_ | 1849409821092085760 |
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| author | Chin-Cheng Lin Shu-Huey Lin |
| author_facet | Chin-Cheng Lin Shu-Huey Lin |
| author_sort | Chin-Cheng Lin |
| collection | DOAJ |
| description | Let {cj} be a null sequence of bounded variation. We give appreciate smoothness and growth conditions on {cj} to obtain the pointwise convergence as well as Lr-convergence of Laguerre series ∑cj𝔏ja. Then, we prove a Hardy-Littlewood type inequality ∫0∞|f(t)|rdt≤C∑j=0∞|cj|rj¯1−r/2 for certain r≤1, where f is the limit function of ∑cj𝔏ja. Moreover, we show that if f(x)∼∑cj𝔏ja is in Lr, r≥1, we have the converse Hardy-Littlewood type inequality ∑j=0∞|cj|rj¯β≤C∫0∞|f(t)|rdt for r≥1 and β<−r/2. |
| format | Article |
| id | doaj-art-79177044381c4a10ab687b69ec035340 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2002-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-79177044381c4a10ab687b69ec0353402025-08-20T03:35:23ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252002-01-0130953354010.1155/S0161171202108234Hardy-Littlewood type inequalities for Laguerre seriesChin-Cheng Lin0Shu-Huey Lin1Department of Mathematics, National Central University, Chung-Li, 320, Taiwan, ChinaDepartment of Mathematics, National Central University, Chung-Li, 320, Taiwan, ChinaLet {cj} be a null sequence of bounded variation. We give appreciate smoothness and growth conditions on {cj} to obtain the pointwise convergence as well as Lr-convergence of Laguerre series ∑cj𝔏ja. Then, we prove a Hardy-Littlewood type inequality ∫0∞|f(t)|rdt≤C∑j=0∞|cj|rj¯1−r/2 for certain r≤1, where f is the limit function of ∑cj𝔏ja. Moreover, we show that if f(x)∼∑cj𝔏ja is in Lr, r≥1, we have the converse Hardy-Littlewood type inequality ∑j=0∞|cj|rj¯β≤C∫0∞|f(t)|rdt for r≥1 and β<−r/2.http://dx.doi.org/10.1155/S0161171202108234 |
| spellingShingle | Chin-Cheng Lin Shu-Huey Lin Hardy-Littlewood type inequalities for Laguerre series International Journal of Mathematics and Mathematical Sciences |
| title | Hardy-Littlewood type inequalities for Laguerre series |
| title_full | Hardy-Littlewood type inequalities for Laguerre series |
| title_fullStr | Hardy-Littlewood type inequalities for Laguerre series |
| title_full_unstemmed | Hardy-Littlewood type inequalities for Laguerre series |
| title_short | Hardy-Littlewood type inequalities for Laguerre series |
| title_sort | hardy littlewood type inequalities for laguerre series |
| url | http://dx.doi.org/10.1155/S0161171202108234 |
| work_keys_str_mv | AT chinchenglin hardylittlewoodtypeinequalitiesforlaguerreseries AT shuhueylin hardylittlewoodtypeinequalitiesforlaguerreseries |