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 $$\int\limits_{\{M_g^{+}(f)>\lambda\}}\widetilde{\varphi}\left(\frac{\lambda}{\omega_{3}(x)\omega_{4}(x)}\right)\omega_{4}(x)\,dx\leq C_1\int\limits_{-\infty}^{+\infty}\widet...
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| Datum: | 2023 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2023
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7062 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: | |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | UDC 517.5
We obtain some necessary and sufficient conditions for a weighted weak-type inequality of the form $$\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. |
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| DOI: | 10.37863/umzh.v75i5.7062 |