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Сиб. матем. журн., 2009, том 50, номер 6, страницы 1391–1400 (Mi smj2058)  

Эта публикация цитируется в 52 научных статьях (всего в 52 статьях)

Операторы интегрального типа из пространства со смешанной нормой в пространство типа Блоха на единичном шаре

С. Стевич

Mathematical Institute of the Serbian Academy of Sciences, Beograd, Serbia

Аннотация: Пусть $\mathbb B$ – единичный шар в $\mathbb C^n$ и $H(\mathbb B)$ – пространство голоморфных функций на $\mathbb B$. Определим оператор интегрального типа на $H(\mathbb B)$, полагая
$$ I^g_\varphi(f)(z)=\int^1_0\mathrm{Re}f(\varphi(tz))g(tz) \frac{dt}t,\qquad z\in\mathbb B, $$
где $g\in H(\mathbb B)$, $g(0)=0$ и $\varphi$ – голоморфное отображение $\mathbb B$. Изучены ограниченность и компактность этого оператора из пространства со смешанной нормой $H(p,q,\phi)(\mathbb B)$ в пространство типа Блоха $\mathscr B_\mu(\mathbb B)$.

Ключевые слова: оператор интегрального типа, пространство со смешанной нормой, пространство типа Блоха, ограниченность, компактность.

Полный текст: PDF файл (334 kB)
Список литературы: PDF файл   HTML файл

Англоязычная версия:
Siberian Mathematical Journal, 2009, 50:6, 1098–1105

Реферативные базы данных:

УДК: 517.98
Статья поступила: 08.04.2008

Образец цитирования: С. Стевич, “Операторы интегрального типа из пространства со смешанной нормой в пространство типа Блоха на единичном шаре”, Сиб. матем. журн., 50:6 (2009), 1391–1400; Siberian Math. J., 50:6 (2009), 1098–1105

Цитирование в формате AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    Эта публикация цитируется в следующих статьяx:
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    9. Jiang Zhi Jie, Stević S., “Compact differences of weighted composition operators from weighted Bergman spaces to weighted-type spaces”, Appl. Math. Comput., 217:7 (2010), 3522–3530  crossref  mathscinet  zmath  isi  scopus
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    22. Zhang L., Zhou Z.-H., “Generalized Composition Operator From Bloch-Type Spaces to Mixed-Norm Space on the Unit Ball”, J. Math. Inequal., 6:4 (2012), 523–532  crossref  mathscinet  zmath  isi  scopus
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    51. Zhu X., “Generalized Weighted Composition Operators on Weighted Bergman Spaces, II”, Math. Inequal. Appl., 22:3 (2019), 1055–1066  crossref  mathscinet  zmath  isi  scopus
    52. Liu Y., Yu Ya., “the Product-Type Operators From Logarithmic Bloch Spaces to Zygmund-Type Spaces”, Filomat, 33:12 (2019), 3639–3653  crossref  mathscinet  isi  scopus
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