TY  - JOUR
T1  - AN INTEGRAL TYPE OPERATOR ON $S^p$ SPACES AND ITS ESSENTIAL NORM
AU  - Hassanlou, Mostafa
AU  - Safarzadeh, Mina
AU  - Ettefagh, Mina
AU  - Zeinalabedini Charandabi, Zohreh
PY  - 2025
DA  - September
Y2  - 2025
JF  - TWMS Journal of Applied and Engineering Mathematics
JO  - JAEM
PB  - Işık University Press
WT  - DergiPark
SN  - 2146-1147
SP  - 2229
EP  - 2238
VL  - 15
IS  - 9
LA  - en
AB  - Given two analytic functions $\lambda: \mathbf{D} \rightarrow \mathbf{D}$ and $\nu: \mathbf{D} \rightarrow \mathbb{C}$  and $n \in \mathbb{N}_0$, we study boundedness of the integral-type operator $C_{\lambda,\nu}^n$ acting from derivative Hardy space into Zygmund space. We also get an approximation for the essential norm of this operator. A characterization for compactness of the operator can be obtained from the essential norm.
KW  - Hardy space.
KW  - Integral-type operator
KW  - Essential norm
KW  - Zygmund type space
CR  - Abkar, A.  and Babaei, A., (2024),  Composition-Differentiation Operators on Derivative Hardy Spaces, J. Math.,  2024, Article ID 8222237, 6 pages.
CR  - Al-Rawashdeh, W., (2024), Volterra-composition operators acting on $S^p$ spaces and weighted Zygmund spaces, Eur. J.  Pure  Appl. Math.,  17(2), pp. 931-944.
CR  - Aleman, A.  and  Siskakkis, A. G., (1995),  An integral operator on $H^p$, Complex Variables, Theory and Application: An International Journal 28, pp.  149-158.
CR  - Aleman, A.  and  Siskakkis, A. G., (1997), Integral operators on Bergman spaces, Indiana U. Math. J.,  46, pp. 337-356.
CR  - Alighadr, A.,  Vaezi, H. and Hassanlou, M., (2022), Essential norm of the generalized integration operator from Zygmund space into weighted Dirichlet type space, Sahand Commun. Math. Anal., 19(2), pp. 33-47.
CR  - Contreras M. D.  and Hernandez-Diaz, A.G., (2004), Weighted composition operators on spaces of functions with derivative in a Hardy space, J. Oper. Theory, 52, pp. 173-184.
CR  - Cowen, C. C.  and MacCluer B. D., (1995), Composition operators on spaces of analytic functions, Studies in Advanced Mathematics. CRC Press, Boca Raton.
CR  - Duren P., (1973), Theory of $H^p$ spaces, Academic Press, New York.
CR  - Hassanlou M. and Abbasi E., (2023), Weighted composition, Volterra and integral operators on Hardy Zygmund-type spaces, J. Math. Ext., 17(8), pp. 1-11.
CR  - Hassanlou M.,  Abbasi E. and  Nasresfahani, S., (2023), n-th derivative Hardy spaces and weighted differentiation composition operators, Iran. J. Sci., 47(4), pp.  1351-1358.
CR  - Hu, N., (2021),  Weighted composition operators from derivative Hardy spaces into n-th weighted-type spaces, J. Math., 2021, Article ID 4398397, 8 pages.
CR  - Li, S.  and Stevic, S., (2008), Generalized composition operators on Zygmund spaces and Bloch type spaces, J. Math. Anal. Appl., 338, pp. 1282-1295
CR  - Liu, J.,  Lin, Q.  and  Wu, Y., (2018), Volterra type operators on $S^p (\mathbb{D})$ spaces, J. Math. Anal. Appl., 461, pp.  1100-1114.
CR  - MacCluer, B. D., (1987), Composition operators on $S^p$, Houston J. Math., 13,  pp. 245-254.
CR  - Manavi, A., Hassanlou M.  and Vaezi, H.,  (2023), Essential norm of generalized integral type operator from $Q_K(p,q)$ to Zygmund Spaces, Filomat, 37(16), pp. 5273-5282.
CR  - Pommerenke, C., (1977), Schlichte Funktionen und analytische Funktionen von Beschrankter mittlerer Oszillation, Comment. Math. Helv., 52, pp. 591-602.
CR  - Roan, R.,  (1978), Composition operators on the space of functions with $H^p$-derivative, Houston J.  Math.,  4, pp. 423-438.
CR  - Xie, H.,  Liu, J. and Wu, Y.,  (2021),  Weighted composition operators on spaces of functions with derivative in a Bergman space, Ann. Funct. Anal.,  12(24),  article number 24.
CR  - Xie, H.,  Liu, J. and Ponnusamy, S., (2023), Volterra-type operators on the minimal Möbius-invariant space, Canad. Math. Bull.,  66(2), pp.  509-524
CR  - Ye, S.   and Zhuo, Z., (2013), Weighted composition operators from Hardy to Zygmund type spaces, Abstr.  Appl. Anal. 2013, Article ID 365286.
CR  - Zhu, X., (2012), An integral-type operator from $H^{\infty}$ to Zygmund-type spaces, Bull. Malays. Math. Sci. Soc.,  35, pp. 679-686.
UR  - https://dergipark.org.tr/en/pub/twmsjaem/issue//1792055
L1  - https://dergipark.org.tr/en/download/article-file/5278507
ER  -