On the Multilinear Fractional Transforms
In this paper we first introduce multilinear fractional wavelet transform on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi&g...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/5/740 |
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| author | Öznur Kulak |
| author_facet | Öznur Kulak |
| author_sort | Öznur Kulak |
| collection | DOAJ |
| description | In this paper we first introduce multilinear fractional wavelet transform on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>n</mi></msup><mo>×</mo><msubsup><mi mathvariant="double-struck">R</mi><mrow><mo>+</mo></mrow><mi>n</mi></msubsup></mrow></semantics></math></inline-formula> using Schwartz functions, i.e., infinitely differentiable complex-valued functions, rapidly decreasing at infinity. We also give multilinear fractional Fourier transform and prove the Hausdorff–Young inequality and Paley-type inequality. We then study boundedness of the multilinear fractional wavelet transform on Lebesgue spaces and Lorentz spaces. |
| first_indexed | 2024-03-10T12:04:52Z |
| format | Article |
| id | doaj.art-8c71f34d387b4a5da4a242849289edd0 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T12:04:52Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-8c71f34d387b4a5da4a242849289edd02023-11-21T16:41:20ZengMDPI AGSymmetry2073-89942021-04-0113574010.3390/sym13050740On the Multilinear Fractional TransformsÖznur Kulak0Department of Mathematics, Faculty of Arts and Sciences, Amasya University, Amasya 05100, TurkeyIn this paper we first introduce multilinear fractional wavelet transform on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>n</mi></msup><mo>×</mo><msubsup><mi mathvariant="double-struck">R</mi><mrow><mo>+</mo></mrow><mi>n</mi></msubsup></mrow></semantics></math></inline-formula> using Schwartz functions, i.e., infinitely differentiable complex-valued functions, rapidly decreasing at infinity. We also give multilinear fractional Fourier transform and prove the Hausdorff–Young inequality and Paley-type inequality. We then study boundedness of the multilinear fractional wavelet transform on Lebesgue spaces and Lorentz spaces.https://www.mdpi.com/2073-8994/13/5/740multilinear fractional wavelet transformmultilinear fractional Fourier transformSchwartz functionsLebesgue spacesLorentz spaces |
| spellingShingle | Öznur Kulak On the Multilinear Fractional Transforms Symmetry multilinear fractional wavelet transform multilinear fractional Fourier transform Schwartz functions Lebesgue spaces Lorentz spaces |
| title | On the Multilinear Fractional Transforms |
| title_full | On the Multilinear Fractional Transforms |
| title_fullStr | On the Multilinear Fractional Transforms |
| title_full_unstemmed | On the Multilinear Fractional Transforms |
| title_short | On the Multilinear Fractional Transforms |
| title_sort | on the multilinear fractional transforms |
| topic | multilinear fractional wavelet transform multilinear fractional Fourier transform Schwartz functions Lebesgue spaces Lorentz spaces |
| url | https://www.mdpi.com/2073-8994/13/5/740 |
| work_keys_str_mv | AT oznurkulak onthemultilinearfractionaltransforms |