Summation of Multiple Fourier Series in Matrix Weighted -Spaces
This paper is concerned with rectangular summation of multiple Fourier series in matrix weighted -spaces. We introduce a product Muckenhoupt condition for matrix weights and prove that rectangular Fourier partial sums converge in the corresponding matrix weighted space , , if and only if the weigh...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/135245 |
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| _version_ | 1849409341288873984 |
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| author | Morten Nielsen |
| author_facet | Morten Nielsen |
| author_sort | Morten Nielsen |
| collection | DOAJ |
| description | This paper is concerned with rectangular summation of multiple Fourier series in matrix weighted -spaces. We introduce a product Muckenhoupt condition for matrix weights and prove that rectangular Fourier partial sums converge in the corresponding matrix weighted space , , if and only if the weight satisfies the product Muckenhoupt condition. The same result is shown to hold true for other summation methods such as Cesàro and summation with the Jackson kernel. |
| format | Article |
| id | doaj-art-7553e87dece04de5ac50abb1b2a9119c |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-7553e87dece04de5ac50abb1b2a9119c2025-08-20T03:35:32ZengWileyJournal of Mathematics2314-46292314-47852013-01-01201310.1155/2013/135245135245Summation of Multiple Fourier Series in Matrix Weighted -SpacesMorten Nielsen0Department of Mathematical Sciences, Aalborg University, Fredrik Bajers Vej 7G, 9220 Aalborg East, DenmarkThis paper is concerned with rectangular summation of multiple Fourier series in matrix weighted -spaces. We introduce a product Muckenhoupt condition for matrix weights and prove that rectangular Fourier partial sums converge in the corresponding matrix weighted space , , if and only if the weight satisfies the product Muckenhoupt condition. The same result is shown to hold true for other summation methods such as Cesàro and summation with the Jackson kernel.http://dx.doi.org/10.1155/2013/135245 |
| spellingShingle | Morten Nielsen Summation of Multiple Fourier Series in Matrix Weighted -Spaces Journal of Mathematics |
| title | Summation of Multiple Fourier Series in Matrix Weighted -Spaces |
| title_full | Summation of Multiple Fourier Series in Matrix Weighted -Spaces |
| title_fullStr | Summation of Multiple Fourier Series in Matrix Weighted -Spaces |
| title_full_unstemmed | Summation of Multiple Fourier Series in Matrix Weighted -Spaces |
| title_short | Summation of Multiple Fourier Series in Matrix Weighted -Spaces |
| title_sort | summation of multiple fourier series in matrix weighted spaces |
| url | http://dx.doi.org/10.1155/2013/135245 |
| work_keys_str_mv | AT mortennielsen summationofmultiplefourierseriesinmatrixweightedspaces |