Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces
We characterize the set of functions for which strong summability holds at each Lebesgue point. More exactly, if f is in the Wiener amalgam space W(L1,lq)(R) and f is almost everywhere locally bounded, or f∈W(Lp,lq)(R) (1<p<∞,1≤q<∞), then strong θ-summability holds at each Lebesgue point o...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2015/420750 |
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| author | Ferenc Weisz |
| author_facet | Ferenc Weisz |
| author_sort | Ferenc Weisz |
| collection | DOAJ |
| description | We characterize the set of functions for which strong summability holds at each Lebesgue point. More exactly, if f is in the Wiener amalgam space W(L1,lq)(R) and f is almost everywhere locally bounded, or f∈W(Lp,lq)(R) (1<p<∞,1≤q<∞), then strong θ-summability holds at each Lebesgue point of f. The analogous results are given for Fourier series, too. |
| format | Article |
| id | doaj-art-eb0bfe6b495f4137bf98d59079044ac1 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-eb0bfe6b495f4137bf98d59079044ac12025-02-03T05:51:24ZengWileyJournal of Function Spaces2314-88962314-88882015-01-01201510.1155/2015/420750420750Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam SpacesFerenc Weisz0Department of Numerical Analysis, Eötvös L. University, Pázmány P. Sétány 1/C, Budapest 1117, HungaryWe characterize the set of functions for which strong summability holds at each Lebesgue point. More exactly, if f is in the Wiener amalgam space W(L1,lq)(R) and f is almost everywhere locally bounded, or f∈W(Lp,lq)(R) (1<p<∞,1≤q<∞), then strong θ-summability holds at each Lebesgue point of f. The analogous results are given for Fourier series, too.http://dx.doi.org/10.1155/2015/420750 |
| spellingShingle | Ferenc Weisz Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces Journal of Function Spaces |
| title | Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces |
| title_full | Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces |
| title_fullStr | Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces |
| title_full_unstemmed | Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces |
| title_short | Strong Summability of Fourier Transforms at Lebesgue Points and Wiener Amalgam Spaces |
| title_sort | strong summability of fourier transforms at lebesgue points and wiener amalgam spaces |
| url | http://dx.doi.org/10.1155/2015/420750 |
| work_keys_str_mv | AT ferencweisz strongsummabilityoffouriertransformsatlebesguepointsandwieneramalgamspaces |