Composition operators from harmonic $ \mathcal{H}^{\infty} $ space into harmonic Zygmund space

Munirah Aljuaid; Mahmoud Ali Bakhit; Munirah Aljuaid; Mahmoud Ali Bakhit

doi:10.3934/math.20231175

AIMS Mathematics

2023, Volume 8, Issue 10: 23087-23107. doi: 10.3934/math.20231175

Previous Article Next Article

Research article Special Issues

Composition operators from harmonic $ \mathcal{H}^{\infty} $ space into harmonic Zygmund space

Munirah Aljuaid ¹,
Mahmoud Ali Bakhit ^{2
,
,}

1.
Department of Mathematics, Faculty of Science, Northern Border University, Arar 73222, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia

Received: 09 April 2023 Revised: 26 June 2023 Accepted: 14 July 2023 Published: 20 July 2023
MSC : 30H30, 31A05

This research paper sought to characterize the boundedness and compactness of composition operators from the space $ \mathcal{H}^{\infty} $ of bounded harmonic mappings into harmonic Zygmund space $ \mathcal{Z}_H $, on the open unit disk. Furthermore, we obtain an estimate of the essential norms of such an operator. These results extends the similar results that were proven for composition operators on analytic function spaces.
- harmonic Zygmund space,
- harmonic $ \mathcal{H}^{\infty} $ space,
- composition operators,
- essential norm
Citation: Munirah Aljuaid, Mahmoud Ali Bakhit. Composition operators from harmonic $ \mathcal{H}^{\infty} $ space into harmonic Zygmund space[J]. AIMS Mathematics, 2023, 8(10): 23087-23107. doi: 10.3934/math.20231175

Related Papers:

Abstract

This research paper sought to characterize the boundedness and compactness of composition operators from the space $ \mathcal{H}^{\infty} $ of bounded harmonic mappings into harmonic Zygmund space $ \mathcal{Z}_H $, on the open unit disk. Furthermore, we obtain an estimate of the essential norms of such an operator. These results extends the similar results that were proven for composition operators on analytic function spaces.

References

[1]	M. Aljuaid, M. A. Bakit, On characterizations of weighted harmonic Bloch mappings and its Carleson measure criteria, J. Funct. Space., 2023 (2023), 8500633. https://doi.org/10.1155/2023/8500633 doi: 10.1155/2023/8500633
[2]	M. Aljuaid, F. Colonna, Characterizations of Bloch-type spaces of harmonic mappings, J. Funct. Space., 2019 (2019), 5687343. https://doi.org/10.1155/2019/5687343 doi: 10.1155/2019/5687343
[3]	M. Aljuaid, F. Colonna, Composition operators on some Banach spaces of harmonic mappings, J. Funct. Space., 2020 (2020), 9034387. https://doi.org/10.1155/2020/9034387 doi: 10.1155/2020/9034387
[4]	M. Aljuaid, F. Colonna, On the harmonic Zygmund spaces, B. Aust. Math. Soc., 101 (2020), 466–476. https://doi.org/10.1017/S0004972720000180 doi: 10.1017/S0004972720000180
[5]	M. Al-Qurashi, S. Rashid, F. Jarad, E. Ali, Ria H. Egami, Dynamic prediction modelling and equilibrium stability of a fractional discrete biophysical neuron model, Results Phys., 48 (2023), 106405. https://doi.org/10.1016/j.rinp.2023.106405 doi: 10.1016/j.rinp.2023.106405
[6]	M. Al-Qurashi, S. Sultana, S. Karim, S. Rashid, F. Jarad, M. S. Alharthi, Identification of numerical solutions of a fractal-fractional divorce epidemic model of nonlinear systems via anti-divorce counseling, AIMS Mathematics, 8 (2023), 5233–5265. https://doi.org/10.3934/math.2023263 doi: 10.3934/math.2023263
[7]	A. K. Alsharidi, S. Rashid, S. K. Elagan, Short-memory discrete fractional difference equation wind turbine model and its inferential control of a chaotic permanent magnet synchronous transformer in time-scale analysis, AIMS Mathematics, 8 (2023), 19097–19120. doilinkhttps://doi.org/10.3934/math.2023975 doi: 10.3934/math.2023975
[8]	S. Axler, P. Bourdon, W. Ramey, Harmonic Function Theory, 2nd Eds., New York: Springer, 2001.
[9]	M. A. Bakhit, Essential norms of Stević–Sharma operators from general Banach spaces into Zygmund-type spaces, J. Math., 2022 (2022), 1230127. https://doi.org/10.1155/2022/1230127 doi: 10.1155/2022/1230127
[10]	C. Boyd, P. Rueda, Isometries of weighted spaces of harmonic functions, Potential Anal., 29 (2008), 37–48. https://doi.org/10.1007/s11118-008-9086-4 doi: 10.1007/s11118-008-9086-4
[11]	R. E. Castillo, J. C. Ramos-Fernández, E. M. Rojas, A new essential norm estimate of composition operators from weighted Bloch space into Bloch spaces, J. Funct. Space., 2013 (2013), 817278. https://doi.org/10.1155/2013/817278 doi: 10.1155/2013/817278
[12]	J. S. Choa, K. J. Izuchi, S. Ohno, Composition Operators on the Space of Bounded Harmonic Functions, Integr. Equ. Oper. Theory, 61 (2008), 167–186. https://doi.org/10.1007/s00020-008-1579-4 doi: 10.1007/s00020-008-1579-4
[13]	F. Colonna, The Bloch constant of bounded harmonic mappings, Indiana U. Math. J., 38 (1989), 829–840.
[14]	C. Cowen, B. MacCluer, Composition operators on spaces of analytic functions, Boca Raton: CRC Press, 1995.
[15]	J. G. Liu, W. H. Zhu, Y. K. Wu, G. H. Jin, Application of multivariate bilinear neural network method to fractional partial differential equations, Results Phys., 47 (2023), 106341. https://doi.org/10.1016/j.rinp.2023.106341 doi: 10.1016/j.rinp.2023.106341
[16]	E. Jordá, A. M. Zarco, Isomorphisms on weighted Banach spaces of harmonic and holomorphic functions, J. Funct. Space., 2013 (2013), 178460. https://doi.org/10.1155/2013/178460 doi: 10.1155/2013/178460
[17]	E. Jordá, A. M. Zarco, Weighted Banach spaces of harmonic functions, RACSAM, 108 (2014), 405–418. https://doi.org/10.1007/s13398-012-0109-z doi: 10.1007/s13398-012-0109-z
[18]	A. Kamal, S. A. Abd-Elhafeez, M. Hamza Eissa, On product-type operators between $H^{\infty}$ and Zygmund Spaces, Appl. Math. Inf. Sci., 16 (2022), 623–633. https://doi.org/10.18576/amis/160416 doi: 10.18576/amis/160416
[19]	J. Laitila, H. O. Tylli, Composition operators on vector-valued harmonic functions and Cauchy transforms, Indiana Univ. Math. J., 55 (2006), 719–746.
[20]	W. Lusky, On weighted spaces of harmonic and holomorphic functions, J. Lond. Math. Soc., 51 (1995), 309–320. https://doi.org/10.1112/jlms/51.2.309 doi: 10.1112/jlms/51.2.309
[21]	W. Lusky, On the isomorphism classes of weighted spaces of harmonic and holomorphic functions, Stud. Math., 175 (2006), 19–45. https://doi.org/10.4064/sm175-1-2 doi: 10.4064/sm175-1-2
[22]	S. Rashid, F. Jarad, S. A. A. El-Marouf, S. K. Elagan, Global dynamics of deterministic-stochastic dengue infection model including multi specific receptors via crossover effects, AIMS Mathematics, 8 (2023), 6466–6503. https://doi.org/10.3934/math.2023327 doi: 10.3934/math.2023327
[23]	R. Yoneda, A characterization of the harmonic Bloch space and the harmonic Besov spaces by an oscillation, Proc. Edinburgh Math. Soc., 45 (2002), 229–239. https://doi.org/10.1017/S001309159900142X doi: 10.1017/S001309159900142X

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)