The Stević-Sharma operator on the Lipschitz space into the logarithmic Bloch space
Year 2023,
, 585 - 595, 30.05.2023
Hamid Vaezi
,
Soran Mahmoudfakheh
Abstract
In this paper, we study the boundedness and compactness of the Stević-Sharma operator on the Lipschitz space into the logarithmic Bloch space. Also, we give an estimate for the essential norm of the above operator.
References
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operators from Bloch type spaces to nth weighted-type spaces, Math. Slovaca 70
(1), 71-80, 2020.
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$H^{\infty}$ to $n$th weighted-type spaces, Mediterr. J. Math. 16, Article no:133, 2019.
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$0 < p < 1$. J. Reine Angew. Math. 238, 32-60, 1969.
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2008.
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Bloch spaces to Bloch-type spaces, Georgian Math. J. 20 (4), 671-686, 2013.
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34, 403-439, 1932.
- [13] M. Hassanlou, H. Vaezi and M. Wang, weighted composition operators on weak valued
Bergman spaces and Hardy spaces, Banach J. Math. Anal. 9 (2), 35-43, 2015.
- [14] S. Li, E. Abbasi and H. Vaezi, Weighted composition operators from Bloch-type spaces
to nth weighted-type spacese, Ann. Polon. Math. 124 (1), 93-107, 2020.
- [15] B. Maccluer and R. Zhao, Essential norm of weighted composition operators between
Bloch-type spaces, Rocky M. J. Math. 33 (4), 1437-1458, 2003.
- [16] A. Petrov, Reverse estimates in logarithmic Bloch spaces, Arch. Math. (Basel) 100
(6), 551-560, 2013.
- [17] J. Shapiro, Composition Operators and alassical function theory, Springer-Verlag,
New York, 1993.
- [18] S. Stević, A.K. Sharma and A. Bhat, Products of multiplication, composition and
differentiation operators on weighted Bergman space, Appl. Math. Comput. 217 (20),
8115-8125, 2011.
- [19] M. Tjani, Compact composition operators on some Mobius invariant Banach spaces,
Ph.D. thesis, Michigan State University, 1996.
- [20] H. Vaezi and S. Houdfar, Weighted composition operators between Besov-type spaces,
Hacet. J. Math. Stat. 49 (1), 78-86, 2020.
- [21] H. Vaezi and S. Houdfar, Composition and weighted composition operators from Blochtype
to Besov-type spaces, Math. Reports 22 (3-4), 297-308, 2020.
- [22] S. Ye, Multipliers and cyclic vectors on the weighted Bloch type space, Math. J.
Okayama Univ. 48, 135-143, 2006
- [23] R. Yoneda, The composition operators on weighted Bloch space, Arch. Math. (Basel)
78 (4), 310-317, 2002.
- [24] F. Zhang and Y. Liu, Products of multiplication, composition and differentiation operators
from mixed-norm spaces to weighted-type spaces, Taiwan. J. Math. 18 (6),
1927-1940, 2014.
- [25] K. Zhu, Bloch type spaces of analytic functions, Rocky Mountain J. Math. 23, 1143-
1177, 1993.
Year 2023,
, 585 - 595, 30.05.2023
Hamid Vaezi
,
Soran Mahmoudfakheh
References
- [1] E. Abbasi and H. Vaezi, Estimates of essential norm of generalized weighted composition
operators from Bloch type spaces to nth weighted-type spaces, Math. Slovaca 70
(1), 71-80, 2020.
- [2] E. Abbasi, H. Vaezi and S. Li, Essential norm of weighted composition operators from
$H^{\infty}$ to $n$th weighted-type spaces, Mediterr. J. Math. 16, Article no:133, 2019.
- [3] J. Arazy, Multipliers of Bloch functions, University of Haifa Mathematics Publications
Series 54, 1982.
- [4] K.R.M. Attele, Toeplitz and Hankel operators on Bergman one space, Hokkaido Math.
J. 21 (2), 279-293, 1992.
- [5] R.E. Castillo, D.D. Clahane, J.F.F. Lopez and J.C.R. Fernndez, Composition operators
from logarithmic Bloch spaces to weighted Bloch spaces, Appl. Math. Comput.
219 (12), 6692-6706, 2013.
- [6] F. Colonna and S. Li, Weighted composition operators from the Lipschitz space into
the Zygmund space, MIA, Math. Inequal. Appl., Article ID 48478, 2007.
- [7] C.C. Cowen and B. MacCluer, Composition operators on spaces of analytic functions,
Stud. Adv. Math., CRC Press, Boca Raton, 1995.
- [8] P.L. Duren, Theory of $H^{p}$ spaces, Academic press, New York, 1970.
- [9] P.L. Duren and B. W. Romberg, Shileds, A.L., Linear functionals on $H^{p}$ spaces with
$0 < p < 1$. J. Reine Angew. Math. 238, 32-60, 1969.
- [10] P. Galanopoulos, On blog to $Q_{p}$ log pullbacks, J. Math. Anal. Appl. 337 (1), 712-725,
2008.
- [11] A.J. Garcia Ortiz and J.C. Ramos-Fernàndez, Composition operators from logarithmic
Bloch spaces to Bloch-type spaces, Georgian Math. J. 20 (4), 671-686, 2013.
- [12] G.H. Hardy and J.E. Littlewood, Some properties of fractional integrals II, Math. Z.
34, 403-439, 1932.
- [13] M. Hassanlou, H. Vaezi and M. Wang, weighted composition operators on weak valued
Bergman spaces and Hardy spaces, Banach J. Math. Anal. 9 (2), 35-43, 2015.
- [14] S. Li, E. Abbasi and H. Vaezi, Weighted composition operators from Bloch-type spaces
to nth weighted-type spacese, Ann. Polon. Math. 124 (1), 93-107, 2020.
- [15] B. Maccluer and R. Zhao, Essential norm of weighted composition operators between
Bloch-type spaces, Rocky M. J. Math. 33 (4), 1437-1458, 2003.
- [16] A. Petrov, Reverse estimates in logarithmic Bloch spaces, Arch. Math. (Basel) 100
(6), 551-560, 2013.
- [17] J. Shapiro, Composition Operators and alassical function theory, Springer-Verlag,
New York, 1993.
- [18] S. Stević, A.K. Sharma and A. Bhat, Products of multiplication, composition and
differentiation operators on weighted Bergman space, Appl. Math. Comput. 217 (20),
8115-8125, 2011.
- [19] M. Tjani, Compact composition operators on some Mobius invariant Banach spaces,
Ph.D. thesis, Michigan State University, 1996.
- [20] H. Vaezi and S. Houdfar, Weighted composition operators between Besov-type spaces,
Hacet. J. Math. Stat. 49 (1), 78-86, 2020.
- [21] H. Vaezi and S. Houdfar, Composition and weighted composition operators from Blochtype
to Besov-type spaces, Math. Reports 22 (3-4), 297-308, 2020.
- [22] S. Ye, Multipliers and cyclic vectors on the weighted Bloch type space, Math. J.
Okayama Univ. 48, 135-143, 2006
- [23] R. Yoneda, The composition operators on weighted Bloch space, Arch. Math. (Basel)
78 (4), 310-317, 2002.
- [24] F. Zhang and Y. Liu, Products of multiplication, composition and differentiation operators
from mixed-norm spaces to weighted-type spaces, Taiwan. J. Math. 18 (6),
1927-1940, 2014.
- [25] K. Zhu, Bloch type spaces of analytic functions, Rocky Mountain J. Math. 23, 1143-
1177, 1993.