An analysis of the convergence problem of a function in Sobolev and generalized Zygmund norms using product operator
Abstract In this paper, we delve into the convergence challenges concerning a function f represented as a Fourier series within Sobolev and generalized Zygmund norms. Our approach involves utilizing the deferred Nörlund–deferred Cesàro product ( D h μ d μ ( N p , q ) D g μ h μ ( C ) $D_{h_{\mu}}^{d_...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2025-03-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-025-03284-9 |
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| Summary: | Abstract In this paper, we delve into the convergence challenges concerning a function f represented as a Fourier series within Sobolev and generalized Zygmund norms. Our approach involves utilizing the deferred Nörlund–deferred Cesàro product ( D h μ d μ ( N p , q ) D g μ h μ ( C ) $D_{h_{\mu}}^{d_{ \mu}}(N^{p,q})D_{g_{\mu}}^{h_{\mu}}(C)$ ) means of Fourier series in order to examine this convergence phenomenon. Further, we conduct a comparative analysis of the convergence outcomes through practical validations. |
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| ISSN: | 1029-242X |