Interpolation of nonlinear integral Urysohn operators in net spaces
In this paper, we study the interpolation properties of the net spaces Np,q(M), in the case when M is a sufficiently general arbitrary system of measurable subsets from Rn. The integral Urysohn operator is considered. This operator generalizes all linear, integral operators, and non-linear integral...
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| Format: | Article |
| Language: | English |
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Academician Ye.A. Buketov Karaganda University
2022-03-01
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| Series: | Қарағанды университетінің хабаршысы. Математика сериясы |
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| Online Access: | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/469 |
| _version_ | 1797372647784316928 |
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| author | A.H. Kalidolday E.D. Nursultanov |
| author_facet | A.H. Kalidolday E.D. Nursultanov |
| author_sort | A.H. Kalidolday |
| collection | DOAJ |
| description |
In this paper, we study the interpolation properties of the net spaces Np,q(M), in the case when M is a sufficiently general arbitrary system of measurable subsets from Rn. The integral Urysohn operator is considered. This operator generalizes all linear, integral operators, and non-linear integral operators. The Urysohn operator is not a quasilinear or subadditive operator. Therefore, the classical interpolation theorems for these operators do not hold. A certain analogue of the Marcinkiewicz-type interpolation theorem for this class of operators is obtained. This theorem allows to obtain, in a sense, a strong estimate for Urysohn operators in net spaces from weak estimates for these operators in net spaces with local nets. For example, in order for the Urysohn integral operator in a net space, where the net is the set of all balls in Rn , it is sufficient for it to be of weak type for net spaces, where the net is concentric balls.
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| first_indexed | 2024-03-08T18:38:52Z |
| format | Article |
| id | doaj.art-4aea685f50ce4d8792af985e33cc3b31 |
| institution | Directory Open Access Journal |
| issn | 2518-7929 2663-5011 |
| language | English |
| last_indexed | 2024-03-08T18:38:52Z |
| publishDate | 2022-03-01 |
| publisher | Academician Ye.A. Buketov Karaganda University |
| record_format | Article |
| series | Қарағанды университетінің хабаршысы. Математика сериясы |
| spelling | doaj.art-4aea685f50ce4d8792af985e33cc3b312023-12-29T10:19:33ZengAcademician Ye.A. Buketov Karaganda UniversityҚарағанды университетінің хабаршысы. Математика сериясы2518-79292663-50112022-03-01105110.31489/2022m1/66-73Interpolation of nonlinear integral Urysohn operators in net spacesA.H. KalidoldayE.D. Nursultanov In this paper, we study the interpolation properties of the net spaces Np,q(M), in the case when M is a sufficiently general arbitrary system of measurable subsets from Rn. The integral Urysohn operator is considered. This operator generalizes all linear, integral operators, and non-linear integral operators. The Urysohn operator is not a quasilinear or subadditive operator. Therefore, the classical interpolation theorems for these operators do not hold. A certain analogue of the Marcinkiewicz-type interpolation theorem for this class of operators is obtained. This theorem allows to obtain, in a sense, a strong estimate for Urysohn operators in net spaces from weak estimates for these operators in net spaces with local nets. For example, in order for the Urysohn integral operator in a net space, where the net is the set of all balls in Rn , it is sufficient for it to be of weak type for net spaces, where the net is concentric balls. http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/469interpolation spacesnet spacesUrysohn integral operators |
| spellingShingle | A.H. Kalidolday E.D. Nursultanov Interpolation of nonlinear integral Urysohn operators in net spaces Қарағанды университетінің хабаршысы. Математика сериясы interpolation spaces net spaces Urysohn integral operators |
| title | Interpolation of nonlinear integral Urysohn operators in net spaces |
| title_full | Interpolation of nonlinear integral Urysohn operators in net spaces |
| title_fullStr | Interpolation of nonlinear integral Urysohn operators in net spaces |
| title_full_unstemmed | Interpolation of nonlinear integral Urysohn operators in net spaces |
| title_short | Interpolation of nonlinear integral Urysohn operators in net spaces |
| title_sort | interpolation of nonlinear integral urysohn operators in net spaces |
| topic | interpolation spaces net spaces Urysohn integral operators |
| url | http://mathematics-vestnik.ksu.kz/index.php/mathematics-vestnik/article/view/469 |
| work_keys_str_mv | AT ahkalidolday interpolationofnonlinearintegralurysohnoperatorsinnetspaces AT ednursultanov interpolationofnonlinearintegralurysohnoperatorsinnetspaces |