Extensions of the Hardy-Littlewood inequalities for Schwarz symmetrization
For a class of functions H:(0,∞)×ℝ+2→ℝ, including discontinuous functions of Carathéodory type, we establish that ∫ℝNH(|x|,u(x),v(x))dx≤∫ℝNH(|x|,u*(x),v*(x))dx, where u*(x) and v*(x) denote the Schwarz symmetrizations of nonnegative functions u and v.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204402348 |
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| _version_ | 1841524840592310272 |
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| author | H. Hajaiej C. A. Stuart |
| author_facet | H. Hajaiej C. A. Stuart |
| author_sort | H. Hajaiej |
| collection | DOAJ |
| description | For a class of functions H:(0,∞)×ℝ+2→ℝ, including discontinuous functions of Carathéodory type, we establish that ∫ℝNH(|x|,u(x),v(x))dx≤∫ℝNH(|x|,u*(x),v*(x))dx, where u*(x) and v*(x) denote the Schwarz symmetrizations of nonnegative functions u and v. |
| format | Article |
| id | doaj-art-2a86902d0f16430cba5935cbb3bb5cb4 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2a86902d0f16430cba5935cbb3bb5cb42025-02-03T05:47:10ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004593129315010.1155/S0161171204402348Extensions of the Hardy-Littlewood inequalities for Schwarz symmetrizationH. Hajaiej0C. A. Stuart1Department of Mathematics, University of Virginia, Charlottesville 22902, VA, USAInstitut d'Analyse et Calcul Scientifique (IACS), Faculte des Sciences de Base (FSB), École Polytechnique Fédérale de Lausanne (EPFL), Lausanne 1015, SwitzerlandFor a class of functions H:(0,∞)×ℝ+2→ℝ, including discontinuous functions of Carathéodory type, we establish that ∫ℝNH(|x|,u(x),v(x))dx≤∫ℝNH(|x|,u*(x),v*(x))dx, where u*(x) and v*(x) denote the Schwarz symmetrizations of nonnegative functions u and v.http://dx.doi.org/10.1155/S0161171204402348 |
| spellingShingle | H. Hajaiej C. A. Stuart Extensions of the Hardy-Littlewood inequalities for Schwarz symmetrization International Journal of Mathematics and Mathematical Sciences |
| title | Extensions of the Hardy-Littlewood inequalities for Schwarz symmetrization |
| title_full | Extensions of the Hardy-Littlewood inequalities for Schwarz symmetrization |
| title_fullStr | Extensions of the Hardy-Littlewood inequalities for Schwarz symmetrization |
| title_full_unstemmed | Extensions of the Hardy-Littlewood inequalities for Schwarz symmetrization |
| title_short | Extensions of the Hardy-Littlewood inequalities for Schwarz symmetrization |
| title_sort | extensions of the hardy littlewood inequalities for schwarz symmetrization |
| url | http://dx.doi.org/10.1155/S0161171204402348 |
| work_keys_str_mv | AT hhajaiej extensionsofthehardylittlewoodinequalitiesforschwarzsymmetrization AT castuart extensionsofthehardylittlewoodinequalitiesforschwarzsymmetrization |