On the Boundedness of Singular Integral Operators in Symmetric Spaces
We consider the integral convolution operators \(T_\varepsilon f\left( x \right) = \int\limits_{|x - y| > \varepsilon } {k\left( {x - y} \right)f\left( y \right)dy}\) defined on spaces of functions of several real variables. For the kernels k(x) satisfying the Hörmander condition, we esta...
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| Datum: | 2000 |
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Institute of Mathematics, NAS of Ukraine
2000
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510627967008768 |
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| author | Peleshenko, B. I. Пелешенко, Б. И. Пелешенко, Б. И. |
| author_facet | Peleshenko, B. I. Пелешенко, Б. И. Пелешенко, Б. И. |
| author_sort | Peleshenko, B. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:30:08Z |
| description | We consider the integral convolution operators \(T_\varepsilon f\left( x \right) = \int\limits_{|x - y| > \varepsilon } {k\left( {x - y} \right)f\left( y \right)dy}\) defined on spaces of functions of several real variables. For the kernels k(x) satisfying the Hörmander condition, we establish necessary and sufficient conditions under which the operators {T ε} are uniformly bounded from Lorentz spaces into Marcinkiewicz spaces. |
| first_indexed | 2026-03-24T03:00:01Z |
| format | Article |
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| id | umjimathkievua-article-4500 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:00:01Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/84/cf74cecebd6efc2539fc935f7af3d384.pdf |
| spelling | umjimathkievua-article-45002020-03-18T20:30:08Z On the Boundedness of Singular Integral Operators in Symmetric Spaces Об ограниченности сингулярных интегральных операторов в симметричных пространствах Peleshenko, B. I. Пелешенко, Б. И. Пелешенко, Б. И. We consider the integral convolution operators \(T_\varepsilon f\left( x \right) = \int\limits_{|x - y| > \varepsilon } {k\left( {x - y} \right)f\left( y \right)dy}\) defined on spaces of functions of several real variables. For the kernels k(x) satisfying the Hörmander condition, we establish necessary and sufficient conditions under which the operators {T ε} are uniformly bounded from Lorentz spaces into Marcinkiewicz spaces. Розглядаються інтегральні оператори згортки $$T_\varepsilon f\left( x \right) = \int\limits_{|x - y| > \varepsilon } {k\left( {x - y} \right)f\left( y \right)dy}$$ задані на просторах функцій декількох дійсних змінних. Для ядер $k(x)$, які задовольняють умову Хермандера, одержано необхідні та достатні умови рівномірної обмеженості операторів $\{T_{ε}\} $ з просторів Лоренца в простори Марцінкевича. Institute of Mathematics, NAS of Ukraine 2000-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4500 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 7 (2000); 988-993 Український математичний журнал; Том 52 № 7 (2000); 988-993 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4500/5704 https://umj.imath.kiev.ua/index.php/umj/article/view/4500/5705 Copyright (c) 2000 Peleshenko B. I. |
| spellingShingle | Peleshenko, B. I. Пелешенко, Б. И. Пелешенко, Б. И. On the Boundedness of Singular Integral Operators in Symmetric Spaces |
| title | On the Boundedness of Singular Integral Operators in Symmetric Spaces |
| title_alt | Об ограниченности сингулярных интегральных операторов в симметричных пространствах |
| title_full | On the Boundedness of Singular Integral Operators in Symmetric Spaces |
| title_fullStr | On the Boundedness of Singular Integral Operators in Symmetric Spaces |
| title_full_unstemmed | On the Boundedness of Singular Integral Operators in Symmetric Spaces |
| title_short | On the Boundedness of Singular Integral Operators in Symmetric Spaces |
| title_sort | on the boundedness of singular integral operators in symmetric spaces |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4500 |
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