Research Article
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Year 2024, Volume: 53 Issue: 5, 1378 - 1392, 15.10.2024
https://doi.org/10.15672/hujms.1299653

Abstract

References

  • [1] F. Colona and N. Hmidouch, Weighted composition operators on iterated weighted type Banach spaces of analytic funcitons, Complex Anal. Oper. Theory 13, 1989- 2016, 2019.
  • [2] F. Colona and S. Li, Weighted composition operators from the Bloch space and the analytic Besov spaces into the Zygmund space, J. Oper. 2013, Article ID 154029, 2013.
  • [3] L. Comtel, Advanced combinatiorics: The Art of Finite and Infinite Expansions. D Reidel Publishing compony, Dordrecht. D. Reidel, Dordrecht, 1974.
  • [4] C. Cowen and B. MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Pres, Boca Raton, 1995.
  • [5] M. Hassanlou and A. Sanatpour, New characterization for the essential norms of generalized weighted composition operators between Zygmund type spaces, Abstr. App. Anal. 2021, Article ID 8831128, 2021.
  • [6] O. Hyvarinen and I. Nieminen, Weighted composition followed by differentiation between Bloch-type spaces, Rev. Mat. Complut. 27, 641-656, 2014.
  • [7] Z. Jiang, Product type operators from area Nevanlina spaces to Bloch-Orlicz spaces, Ital. J. pure Appl. Math. 40, 227-243, 2018.
  • [8] W. Johnson, The curious history of Faá di Bruno’s formula, Am. Math. Mon. 109 (3), 217-234, 2002.
  • [9] S. Li and S. Stevic, Composition followed by differentiation between Bloch-type spaces, J. Comput. Anal. Appl. 9 (2), 195-205, 2007.
  • [10] S. Li and S. Stevic, Generalized weighted composition operators from $\alpha$-Bloch spaces into weighted type spaces, J. Inequal. Appl. 265, 1-12, 2015.
  • [11] B. D. MacCluer and R. Zhao, ssential norm of weighted composition operators between Bloch type spaces, Rocky Mountain J. Math. 33 (4), 1437-1458, 2003.
  • [12] J. S. Manhas and R. Zhao, New estimates of essential norms of weighted composition operators between Bloch type spaces, J. Math. Anal. App. 389, 32-47, 2012.
  • [13] A. Montes-Rodriguez, Weighted composition operators on weighted Banach spaces of analytic functions, J. London Math. Soc. 61 (3), 872-884, 2000.
  • [14] S. Nasresfahani and E. Abbasi, Product type operators on weak vector valued $\alpha$-Besov spaces, Turkish j. Math. 64 (4), 1210-1223, 2022.
  • [15] Sh. Ohno, K. Stroethoff and R. Zhao, Weighted composition operators between Blochtype spaces, Rocky Mountan J. Math. 33 (1)„ 191-215, 2003.
  • [16] J. Riordan, An Introduction to Combinatorial Analysis, J. Wiley and Sons, New york, 1958.
  • [17] S. Stević, Composition operators from the weighted Bergman spaces to the nth weighted spaces on the unit disk, Discrete Dyn. Nat. Soc. 2009, Articcle ID 742019, 11 pages, 2009.
  • [18] S. Stević, On an integral operator from the zygmund space to the Bloch type space on the unit ball, Glasg. H. Math. 51, 275-287, 2009.
  • [19] S. Stević, Weighted differentiation composition operators from $H^\infty$ and Bloch spaces to nth weighted-type spaces on the unit disk, J. Appl. Math. Comput. 216 (12), 3634- 3641, 2010.
  • [20] S. Stević, AK. Sharma and A. Bhat, Product of multiplication composition and differentiation operators on weighted Bergman spaces, Appl. Math. Comput. 217, 8115- 8125, 2011.
  • [21] H. Vaezi and S. Houdfar, Weigted composition operatros between Besov-type spaces, Hacet. J. Math. Stat. 49 (1), 78-86, 2020.
  • [22] M. Wang, Riemann-stieltjes operators between vector velued weighted Bloch spaces, J. Ineq. Appl. 2008 348208, 2008.
  • [23] Y. Wu and H. Wuhan, Products of differentiation and composition operators on the Bloch space Collect. Math. 63, 93-107, 2012.
  • [24] Y. YU and Y. Liu, On Stević type operators from $H^\infty$ spaces to the logarithmic Bloch spaces, Complex Anal. Oper. Theory. 9, 1759-1780, 2015.
  • [25] K. Zhu, Bloch type spaces of analytic functions, Rocky mountain J. Math., 23 (3), 1143-1177, 1993.
  • [26] K. Zhu, Spaces of Holomorphic functions in the Unit Ball, Springer, New York, 2005.
  • [27] X. Zhu and J. Du, Weighted composition operators from weighted Bergman spaces to Stević-type spaces, Math. Inequal. App. 22 (1), 361-376, 2019.

Generalized product-type operators between Bloch-type spaces

Year 2024, Volume: 53 Issue: 5, 1378 - 1392, 15.10.2024
https://doi.org/10.15672/hujms.1299653

Abstract

In this paper, we consider generalized product type operators $D^n uC_\phi$ and $T^n_{u_1,u_2,\phi}$. Then we provide several characterizations, as equivalent statements, for the boundedness and compactness of these operators between Bloch type spaces $\mathcal{B}_\alpha(\mathbb{U})$, for all $0<\alpha<\infty$.

References

  • [1] F. Colona and N. Hmidouch, Weighted composition operators on iterated weighted type Banach spaces of analytic funcitons, Complex Anal. Oper. Theory 13, 1989- 2016, 2019.
  • [2] F. Colona and S. Li, Weighted composition operators from the Bloch space and the analytic Besov spaces into the Zygmund space, J. Oper. 2013, Article ID 154029, 2013.
  • [3] L. Comtel, Advanced combinatiorics: The Art of Finite and Infinite Expansions. D Reidel Publishing compony, Dordrecht. D. Reidel, Dordrecht, 1974.
  • [4] C. Cowen and B. MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Pres, Boca Raton, 1995.
  • [5] M. Hassanlou and A. Sanatpour, New characterization for the essential norms of generalized weighted composition operators between Zygmund type spaces, Abstr. App. Anal. 2021, Article ID 8831128, 2021.
  • [6] O. Hyvarinen and I. Nieminen, Weighted composition followed by differentiation between Bloch-type spaces, Rev. Mat. Complut. 27, 641-656, 2014.
  • [7] Z. Jiang, Product type operators from area Nevanlina spaces to Bloch-Orlicz spaces, Ital. J. pure Appl. Math. 40, 227-243, 2018.
  • [8] W. Johnson, The curious history of Faá di Bruno’s formula, Am. Math. Mon. 109 (3), 217-234, 2002.
  • [9] S. Li and S. Stevic, Composition followed by differentiation between Bloch-type spaces, J. Comput. Anal. Appl. 9 (2), 195-205, 2007.
  • [10] S. Li and S. Stevic, Generalized weighted composition operators from $\alpha$-Bloch spaces into weighted type spaces, J. Inequal. Appl. 265, 1-12, 2015.
  • [11] B. D. MacCluer and R. Zhao, ssential norm of weighted composition operators between Bloch type spaces, Rocky Mountain J. Math. 33 (4), 1437-1458, 2003.
  • [12] J. S. Manhas and R. Zhao, New estimates of essential norms of weighted composition operators between Bloch type spaces, J. Math. Anal. App. 389, 32-47, 2012.
  • [13] A. Montes-Rodriguez, Weighted composition operators on weighted Banach spaces of analytic functions, J. London Math. Soc. 61 (3), 872-884, 2000.
  • [14] S. Nasresfahani and E. Abbasi, Product type operators on weak vector valued $\alpha$-Besov spaces, Turkish j. Math. 64 (4), 1210-1223, 2022.
  • [15] Sh. Ohno, K. Stroethoff and R. Zhao, Weighted composition operators between Blochtype spaces, Rocky Mountan J. Math. 33 (1)„ 191-215, 2003.
  • [16] J. Riordan, An Introduction to Combinatorial Analysis, J. Wiley and Sons, New york, 1958.
  • [17] S. Stević, Composition operators from the weighted Bergman spaces to the nth weighted spaces on the unit disk, Discrete Dyn. Nat. Soc. 2009, Articcle ID 742019, 11 pages, 2009.
  • [18] S. Stević, On an integral operator from the zygmund space to the Bloch type space on the unit ball, Glasg. H. Math. 51, 275-287, 2009.
  • [19] S. Stević, Weighted differentiation composition operators from $H^\infty$ and Bloch spaces to nth weighted-type spaces on the unit disk, J. Appl. Math. Comput. 216 (12), 3634- 3641, 2010.
  • [20] S. Stević, AK. Sharma and A. Bhat, Product of multiplication composition and differentiation operators on weighted Bergman spaces, Appl. Math. Comput. 217, 8115- 8125, 2011.
  • [21] H. Vaezi and S. Houdfar, Weigted composition operatros between Besov-type spaces, Hacet. J. Math. Stat. 49 (1), 78-86, 2020.
  • [22] M. Wang, Riemann-stieltjes operators between vector velued weighted Bloch spaces, J. Ineq. Appl. 2008 348208, 2008.
  • [23] Y. Wu and H. Wuhan, Products of differentiation and composition operators on the Bloch space Collect. Math. 63, 93-107, 2012.
  • [24] Y. YU and Y. Liu, On Stević type operators from $H^\infty$ spaces to the logarithmic Bloch spaces, Complex Anal. Oper. Theory. 9, 1759-1780, 2015.
  • [25] K. Zhu, Bloch type spaces of analytic functions, Rocky mountain J. Math., 23 (3), 1143-1177, 1993.
  • [26] K. Zhu, Spaces of Holomorphic functions in the Unit Ball, Springer, New York, 2005.
  • [27] X. Zhu and J. Du, Weighted composition operators from weighted Bergman spaces to Stević-type spaces, Math. Inequal. App. 22 (1), 361-376, 2019.
There are 27 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Sepideh Nasresfahani 0000-0002-5494-861X

Ebrahim Abbasi 0000-0002-4133-3763

Early Pub Date January 10, 2024
Publication Date October 15, 2024
Published in Issue Year 2024 Volume: 53 Issue: 5

Cite

APA Nasresfahani, S., & Abbasi, E. (2024). Generalized product-type operators between Bloch-type spaces. Hacettepe Journal of Mathematics and Statistics, 53(5), 1378-1392. https://doi.org/10.15672/hujms.1299653
AMA Nasresfahani S, Abbasi E. Generalized product-type operators between Bloch-type spaces. Hacettepe Journal of Mathematics and Statistics. October 2024;53(5):1378-1392. doi:10.15672/hujms.1299653
Chicago Nasresfahani, Sepideh, and Ebrahim Abbasi. “Generalized Product-Type Operators Between Bloch-Type Spaces”. Hacettepe Journal of Mathematics and Statistics 53, no. 5 (October 2024): 1378-92. https://doi.org/10.15672/hujms.1299653.
EndNote Nasresfahani S, Abbasi E (October 1, 2024) Generalized product-type operators between Bloch-type spaces. Hacettepe Journal of Mathematics and Statistics 53 5 1378–1392.
IEEE S. Nasresfahani and E. Abbasi, “Generalized product-type operators between Bloch-type spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 5, pp. 1378–1392, 2024, doi: 10.15672/hujms.1299653.
ISNAD Nasresfahani, Sepideh - Abbasi, Ebrahim. “Generalized Product-Type Operators Between Bloch-Type Spaces”. Hacettepe Journal of Mathematics and Statistics 53/5 (October 2024), 1378-1392. https://doi.org/10.15672/hujms.1299653.
JAMA Nasresfahani S, Abbasi E. Generalized product-type operators between Bloch-type spaces. Hacettepe Journal of Mathematics and Statistics. 2024;53:1378–1392.
MLA Nasresfahani, Sepideh and Ebrahim Abbasi. “Generalized Product-Type Operators Between Bloch-Type Spaces”. Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 5, 2024, pp. 1378-92, doi:10.15672/hujms.1299653.
Vancouver Nasresfahani S, Abbasi E. Generalized product-type operators between Bloch-type spaces. Hacettepe Journal of Mathematics and Statistics. 2024;53(5):1378-92.