پیوندهای مفید
آمار
| تعداد نشریات | 21 |
| تعداد شماره‌ها | 653 |
| تعداد مقالات | 9,524 |
| تعداد مشاهده مقاله | 68,449,135 |
| تعداد دریافت فایل اصل مقاله | 47,909,131 |
Generalized weighted composition operators acting between Dirichlet-type spaces and Bloch-type spaces | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 1، دوره 16، شماره 1، فروردین 2025، صفحه 1-10 اصل مقاله (498.02 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.25200.2950 | ||
| نویسندگان | ||
| Manisha Devi1؛ Kuldip Raj1؛ Ayhan Esi* 2؛ Muhammed Aiyub3 | ||
| 1School of Mathematics Shri Mata Vaishno Devi University Katra-182320, J&K, India | ||
| 2Engineering Faculty Malatya Turgut Ozal University Malatya,44040, Turkey | ||
| 3Department of Mathematics, Bahrain University, P. O. Box-32038, Bahrain | ||
| تاریخ دریافت: 19 آبان 1400، تاریخ بازنگری: 20 شهریور 1402، تاریخ پذیرش: 22 شهریور 1402 | ||
| چکیده | ||
| Let $\mathbb{D}= \{\upsilon\in\mathbb{C}:|\upsilon|<1\}$ be the open unit disk in the complex plane $\mathbb{C}$ and let $H(\mathbb{D})$ be the space of all holomorphic functions on $\mathbb{D}$. For a non-negative integer $n$ and a function $f \in H(\mathbb{D})$, the $n^{th}-$ order differentiation operator is defined as $D^n f = f^{(n)}$. The weighted composition operator together with $n^{th}-$ order differentiation operator give rise to a new operator generally termed as generalized weighted composition operator denoted by $\mathcal{W}^{n}_{\phi,\xi}$ and is defined by \begin{equation*} \mathcal{W}^{n}_{\phi,\xi}f(\upsilon) =\phi(\upsilon)f^{(n)}(\xi(\upsilon)),\quad f\in H(\mathbb{D}); \upsilon\in% \mathbb{D}, \end{equation*} where $\phi\in H(\mathbb{D})$ and $\xi$ is a holomorphic self-map of $\mathbb{D}$. This operator is basically the combination of multiplication operator $M_{\phi}$, composition operator $C_{\xi}$ and $n^{th}-$ order differentiation operator $D^{n}$. We study the boundedness and compactness of this operator between Dirichlet-type spaces and Bloch-type spaces. | ||
| کلیدواژه‌ها | ||
| Dirichlet-type space؛ Bloch-type spaces؛ generalized weighted composition operator؛ boundedness؛ compactness | ||
| مراجع | ||
|
[1] A. Aleman, Hilbert spaces of analytic functions between the Hardy space and the Dirichlet space, Proc. Amer. Math. Soc. 115 (1992), 97–104. [2] H.A. Alsaker, Multipliers of the Dirichlet space, Master’s thesis, Department of Mathematics, The University of Bergen, 2009. [3] N. Arcozzi, R. Rochberg, E.T. Sawyer, and B.D. Wick, The Dirichlet space: a survey, New York J. Math. 17A (2011), 45–86. [4] G. Bao, Z. Lou, R. Qian, and H. Wulan, On multipliers of Dirichlet type spaces, Complex Anal. Oper. Theory 9 (2015), 1701–1732. [5] F. Colonna and S. Li, Weighted composition operators from the minimal Mobius invariant space into the Bloch space, Mediter. J. Math. 10 (2013), 395–409. [6] C.C. Cowen and B.D. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, FL, 1995. [7] M. Devi, A.K. Sharma, and K. Raj, Weighted composition operators from Dirichlet type spaces to some weighted-type spaces, J. Comput. Anal. Appl. 28 (2020), 127–135. [8] M. Devi, A.K. Sharma and K. Raj, Inequalities involving essential norm estimates of product-type operators, J. Math. 2021 (2021), Article ID 8811309, 9 pages. [9] K. Esmaeili and M. Lindstr¨om, Weighted composition operators between Zygmund type spaces and their essential norms, Integral Equ. Oper. Theory 75 (2013), 473–490. [10] M. Essen, H. Wulan, and J. Xiao, Several function-theoretic characterizations of Mobius invariant QK spaces, J. Funct. Anal. 230 (2006), 78–115. [11] Z. J. Jiang, On a class of operators from weighted Bergman spaces to some spaces of analytic functions, Taiwan. J. Math. 15 (2011), 2095–2121. [12] Z. J. Jiang, On a product-type operator from weighted Bergman-Orlicz space to some weighted-type spaces, Appl. Math. Comput. 256 (2015), 37–51. [13] R. Kerman and E. Sawyer, Carleson measures and multipliers of Dirichlet-type spaces, Trans. Amer. Math. Soc. 309 (1988), 87–98. [14] H. Li and X. Fu, A new characterization of generalized weighted composition operators from the Bloch space into the Zygmund space, J. Funct. Spaces Appl. 2013 (2013), Article ID 925901, 6 pages. [15] Y. Liu and Y. Yu, Weighted differentiation composition operators from mixed-norm to Zygmund spaces, Numer. Funct. Anal. Optim. 31(8) (2010), 936–954. [16] Y. Liu and Y. Yu, Composition followed by differentiation between H∞ and Zygmund spaces, Complex. Anal. Oper. Theory, 6 (2012), no. 1, 121–137. [17] S. Ohno, K. Stroethoff, and R. Zhao, Weighted composition operators between Bloch-type spaces, Rocky Mt. J. Math. 33 (2003), 191–215. [18] H. Qu, Y. Liu, and S. Cheng, Weighted differentiation composition operator from logarithmic Bloch spaces to Zygmund-type spaces, Abstr. Appl. Anal. 2014 (2014), Article ID 832713, 14 pages. [19] R. Rochberg and Z. Wu, A new characterization of Dirichlet type spaces and applications, Illinois J. Math. 37 (1993), 101–122. [20] A.H. Sanatpour and M. Hassanlou, Essential norms of weighted differentiation composition operators between Zygmund-type spaces and Bloch-type spaces, Filomat 31 (2017), 2877–2889. [21] D. Stegenga, Multipliers of the Dirichlet space, Illinois J. Math. 24 (1980), 113–139. [22] S. Stevic, Weighted differentiation composition operators from H∞ and Bloch spaces to nth−weighted-type spaces on the unit disk, Appl. Math. Comput. 216 (2010), 3634–3641. [23] G. Taylor, Multipliers on Dα, Trans. Amer. Math. Soc. 123 (1966), 229–240. [24] H. Wulan and J. Zhou, QK and Morrey type spaces, Ann. Acad. Sci. Fenn. Math. 38 (2013), 193–207. [25] H. Wulan and K. Zhu, Lacunary Series in QK Spaces, Stud. Math. 173 (2007), 217–230. [26] L. Yang, Integral operator acting on weighted Dirichlet spaces to Morrey type spaces, Filomat 33 (2019), 3723–3736. [27] Y. Yu and Y. Liu, Weighted differentiation composition operators from H∞ to Zygmund spaces, Integral Transforms Spec. Funct. 22 (2011), 507–520. [28] J.Z. Zhou and Y.T. Wu, Decomposition theorems and conjugate pair in DK spaces, Acta Math. Sinica English Ser. 30 (2014), 1513–1525. | ||
|
آمار تعداد مشاهده مقاله: 626 تعداد دریافت فایل اصل مقاله: 578 |
||