Year 2024,
, 1378 - 1392, 15.10.2024
Sepideh Nasresfahani
,
Ebrahim Abbasi
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,
, 1378 - 1392, 15.10.2024
Sepideh Nasresfahani
,
Ebrahim Abbasi
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.