A weighted weak-type inequality for the one-sided maximal operators
UDC 517.5 We obtain some necessary and sufficient conditions for a weighted weak-type inequality of the form $$\int\limits_{\{M_g^{+}(f)>\lambda\}}\widetilde{\varphi}\left(\frac{\lambda}{\omega_{3}(x)\omega_{4}(x)}\right)\omega_{4}(x)\,dx\leq C_1\int\limits_{-\infty}^{+\infty}\widet...
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| Date: | 2023 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2023
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7062 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512587168350208 |
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| author | Wang, J. Ren, Y. Zhang, E. Wang, J. Ren, Y. Zhang, E. |
| author_facet | Wang, J. Ren, Y. Zhang, E. Wang, J. Ren, Y. Zhang, E. |
| author_sort | Wang, J. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-06-13T15:56:17Z |
| description |
UDC 517.5
We obtain some necessary and sufficient conditions for a weighted weak-type inequality of the form $$\int\limits_{\{M_g^{+}(f)>\lambda\}}\widetilde{\varphi}\left(\frac{\lambda}{\omega_{3}(x)\omega_{4}(x)}\right)\omega_{4}(x)\,dx\leq C_1\int\limits_{-\infty}^{+\infty}\widetilde{\varphi}\left(C_{1}\frac{|f(x)|}{\omega_{1}(x)\omega_{2}(x)}\right)\omega_{2}(x)\,dx$$ to be true, which generalize some known results. |
| doi_str_mv | 10.37863/umzh.v75i5.7062 |
| first_indexed | 2026-03-24T03:31:09Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7062 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:31:09Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-70622023-06-13T15:56:17Z A weighted weak-type inequality for the one-sided maximal operators A weighted weak-type inequality for the one-sided maximal operators Wang, J. Ren, Y. Zhang, E. Wang, J. Ren, Y. Zhang, E. weight, weak type inequality, one-sided maximal operator, Orlicz class UDC 517.5 We obtain some necessary and sufficient conditions for a weighted weak-type inequality of the form $$\int\limits_{\{M_g^{+}(f)>\lambda\}}\widetilde{\varphi}\left(\frac{\lambda}{\omega_{3}(x)\omega_{4}(x)}\right)\omega_{4}(x)\,dx\leq C_1\int\limits_{-\infty}^{+\infty}\widetilde{\varphi}\left(C_{1}\frac{|f(x)|}{\omega_{1}(x)\omega_{2}(x)}\right)\omega_{2}(x)\,dx$$ to be true, which generalize some known results. УДК 517.5 Зважена нерівність слабкого типу для односторонніх максимальних операторів Наведено деякі необхідні й достатні умови для того, щоб виконувалась зважена нерівність слабкого типу $$\int\limits_{\{M_g^{+}(f)>\lambda\}}\widetilde{\varphi}\left(\frac{\lambda}{\omega_{3}(x)\omega_{4}(x)}\right)\omega_{4}(x)\,dx\leq C_1\int\limits_{-\infty}^{+\infty}\widetilde{\varphi}\left(C_{1}\frac{|f(x)|}{\omega_{1}(x)\omega_{2}(x)}\right)\omega_{2}(x)\,dx.$$ Результати, отримані в роботі, узагальнюють деякі відомі результати. Institute of Mathematics, NAS of Ukraine 2023-05-24 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7062 10.37863/umzh.v75i5.7062 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 5 (2023); 712- 720 Український математичний журнал; Том 75 № 5 (2023); 712- 720 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7062/9776 Copyright (c) 2023 Jing Wang |
| spellingShingle | Wang, J. Ren, Y. Zhang, E. Wang, J. Ren, Y. Zhang, E. A weighted weak-type inequality for the one-sided maximal operators |
| title | A weighted weak-type inequality for the one-sided maximal operators |
| title_alt | A weighted weak-type inequality for the one-sided maximal operators |
| title_full | A weighted weak-type inequality for the one-sided maximal operators |
| title_fullStr | A weighted weak-type inequality for the one-sided maximal operators |
| title_full_unstemmed | A weighted weak-type inequality for the one-sided maximal operators |
| title_short | A weighted weak-type inequality for the one-sided maximal operators |
| title_sort | weighted weak-type inequality for the one-sided maximal operators |
| topic_facet | weight weak type inequality one-sided maximal operator Orlicz class |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7062 |
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