( H p − L p ) $(H_{p}-L_{p})$ -Type inequalities for subsequences of Nörlund means of Walsh–Fourier series
Abstract We investigate the subsequence { t 2 n f } $\{t_{2^{n}}f \}$ of Nörlund means with respect to the Walsh system generated by nonincreasing and convex sequences. In particular, we prove that a large class of such summability methods are not bounded from the martingale Hardy spaces H p $H_{p}$...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-04-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-023-02955-9 |
| _version_ | 1827970211559505920 |
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| author | David Baramidze Lars-Erik Persson Kristoffer Tangrand George Tephnadze |
| author_facet | David Baramidze Lars-Erik Persson Kristoffer Tangrand George Tephnadze |
| author_sort | David Baramidze |
| collection | DOAJ |
| description | Abstract We investigate the subsequence { t 2 n f } $\{t_{2^{n}}f \}$ of Nörlund means with respect to the Walsh system generated by nonincreasing and convex sequences. In particular, we prove that a large class of such summability methods are not bounded from the martingale Hardy spaces H p $H_{p}$ to the space w e a k − L p $\mathit{weak-}L_{p} $ for 0 < p < 1 / ( 1 + α ) $0< p<1/(1+\alpha ) $ , where 0 < α < 1 $0<\alpha <1$ . Moreover, some new related inequalities are derived. As applications, some well-known and new results are pointed out for well-known summability methods, especially for Nörlund logarithmic means and Cesàro means. |
| first_indexed | 2024-04-09T18:50:26Z |
| format | Article |
| id | doaj.art-442c064550af42de9ccd72f175295184 |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-09T18:50:26Z |
| publishDate | 2023-04-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-442c064550af42de9ccd72f1752951842023-04-09T11:29:38ZengSpringerOpenJournal of Inequalities and Applications1029-242X2023-04-012023111310.1186/s13660-023-02955-9( H p − L p ) $(H_{p}-L_{p})$ -Type inequalities for subsequences of Nörlund means of Walsh–Fourier seriesDavid Baramidze0Lars-Erik Persson1Kristoffer Tangrand2George Tephnadze3School of Science and Technology, The University of GeorgiaDepartment of Computer Science and Computational Engineering, UiT The Arctic University of NorwayDepartment of Computer Science and Computational Engineering, UiT The Arctic University of NorwaySchool of Science and Technology, The University of GeorgiaAbstract We investigate the subsequence { t 2 n f } $\{t_{2^{n}}f \}$ of Nörlund means with respect to the Walsh system generated by nonincreasing and convex sequences. In particular, we prove that a large class of such summability methods are not bounded from the martingale Hardy spaces H p $H_{p}$ to the space w e a k − L p $\mathit{weak-}L_{p} $ for 0 < p < 1 / ( 1 + α ) $0< p<1/(1+\alpha ) $ , where 0 < α < 1 $0<\alpha <1$ . Moreover, some new related inequalities are derived. As applications, some well-known and new results are pointed out for well-known summability methods, especially for Nörlund logarithmic means and Cesàro means.https://doi.org/10.1186/s13660-023-02955-9Walsh systemNörlund meansCesàro meansNörlund logarithmic meansMartingale Hardy spaceConvergence |
| spellingShingle | David Baramidze Lars-Erik Persson Kristoffer Tangrand George Tephnadze ( H p − L p ) $(H_{p}-L_{p})$ -Type inequalities for subsequences of Nörlund means of Walsh–Fourier series Journal of Inequalities and Applications Walsh system Nörlund means Cesàro means Nörlund logarithmic means Martingale Hardy space Convergence |
| title | ( H p − L p ) $(H_{p}-L_{p})$ -Type inequalities for subsequences of Nörlund means of Walsh–Fourier series |
| title_full | ( H p − L p ) $(H_{p}-L_{p})$ -Type inequalities for subsequences of Nörlund means of Walsh–Fourier series |
| title_fullStr | ( H p − L p ) $(H_{p}-L_{p})$ -Type inequalities for subsequences of Nörlund means of Walsh–Fourier series |
| title_full_unstemmed | ( H p − L p ) $(H_{p}-L_{p})$ -Type inequalities for subsequences of Nörlund means of Walsh–Fourier series |
| title_short | ( H p − L p ) $(H_{p}-L_{p})$ -Type inequalities for subsequences of Nörlund means of Walsh–Fourier series |
| title_sort | h p l p h p l p type inequalities for subsequences of norlund means of walsh fourier series |
| topic | Walsh system Nörlund means Cesàro means Nörlund logarithmic means Martingale Hardy space Convergence |
| url | https://doi.org/10.1186/s13660-023-02955-9 |
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