Weighted inequalities for Hilbert transforms and multiplicators of Fourier transforms
As is well known, invariant operators with a shift can be bounded from Lp into Lq only if 1<p≤q<∞. We show that the case q<p might also hold for weighted spaces. We derive the sufficient conditions for the validity of strong (weak) (p,q) type inequalities for the Hilbert transform...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
1997-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S1025583497000167 |
| _version_ | 1818068156321628160 |
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| author | A. Meskhi V. Kokilashvili |
| author_facet | A. Meskhi V. Kokilashvili |
| author_sort | A. Meskhi |
| collection | DOAJ |
| description | As is well known, invariant operators with a shift can be bounded from Lp into Lq only if 1<p≤q<∞. We show that the case q<p might also hold for weighted spaces. We derive the sufficient conditions for the validity of strong (weak) (p,q) type inequalities for the Hilbert transform when 1<q<p<∞ (q=1,1<p<∞). |
| first_indexed | 2024-12-10T15:35:06Z |
| format | Article |
| id | doaj.art-3daaaac290224339accd316a2b5156f2 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-10T15:35:06Z |
| publishDate | 1997-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-3daaaac290224339accd316a2b5156f22022-12-22T01:43:14ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X1997-01-011323925210.1155/S1025583497000167Weighted inequalities for Hilbert transforms and multiplicators of Fourier transformsA. MeskhiV. KokilashviliAs is well known, invariant operators with a shift can be bounded from Lp into Lq only if 1<p≤q<∞. We show that the case q<p might also hold for weighted spaces. We derive the sufficient conditions for the validity of strong (weak) (p,q) type inequalities for the Hilbert transform when 1<q<p<∞ (q=1,1<p<∞).http://dx.doi.org/10.1155/S1025583497000167Hilbert transform; two-weight inequality; weak and strong type estimates; Fourier transform; multiplier. |
| spellingShingle | A. Meskhi V. Kokilashvili Weighted inequalities for Hilbert transforms and multiplicators of Fourier transforms Journal of Inequalities and Applications Hilbert transform; two-weight inequality; weak and strong type estimates; Fourier transform; multiplier. |
| title | Weighted inequalities for Hilbert transforms and multiplicators of Fourier transforms |
| title_full | Weighted inequalities for Hilbert transforms and multiplicators of Fourier transforms |
| title_fullStr | Weighted inequalities for Hilbert transforms and multiplicators of Fourier transforms |
| title_full_unstemmed | Weighted inequalities for Hilbert transforms and multiplicators of Fourier transforms |
| title_short | Weighted inequalities for Hilbert transforms and multiplicators of Fourier transforms |
| title_sort | weighted inequalities for hilbert transforms and multiplicators of fourier transforms |
| topic | Hilbert transform; two-weight inequality; weak and strong type estimates; Fourier transform; multiplier. |
| url | http://dx.doi.org/10.1155/S1025583497000167 |
| work_keys_str_mv | AT ameskhi weightedinequalitiesforhilberttransformsandmultiplicatorsoffouriertransforms AT vkokilashvili weightedinequalitiesforhilberttransformsandmultiplicatorsoffouriertransforms |