Composition Operators From Harmonic Lipschitz Space Into Weighted Harmonic Zygmund Space

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DOI: https://doi.org/10.28924/2291-8639-21-2023-125
Published: Nov 21, 2023
Cite as:
M. A. Bakhit, N. M. Dahshan, Ranya Tahier, Omniat O. Y. Karrar, Mehreen S. Khan, M. A. Orsud, Composition Operators From Harmonic Lipschitz Space Into Weighted Harmonic Zygmund Space, Int. J. Anal. Appl., 21 (2023), 125.

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M. A. Bakhit, N. M. Dahshan, Ranya Tahier, Omniat O. Y. Karrar, Mehreen S. Khan, M. A. Orsud

Abstract

The paper investigate a necessary and sufficient condition for the composition operator from harmonic Lipschitz spaces LipHα, (0<α<1) into weighted harmonic Zygmund spaces ZHβ, (0<β<∞) to be bounded and compact on the open unit disk. As an application, it estimates the essential norms of such an operator from LipHα into ZHβ spaces.

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References

  1. M. Aljuaid, M.A. Bakhit, On Characterizations of Weighted Harmonic Bloch Mappings and Its Carleson Measure Criteria, J. Funct. Spaces. 2023 (2023), 8500633. https://doi.org/10.1155/2023/8500633.
  2. M. Aljuaid, M.A. Bakhit, Composition Operators From Harmonic H∞ Space Into Harmonic Zygmund Space, AIMS Math. 8 (2023), 23087–23107. https://doi.org/10.3934/math.20231175.
  3. M. Aljuaid, F. Colonna, Characterizations of Bloch-Type Spaces of Harmonic Mappings, J. Funct. Spaces. 2019 (2019), 5687343. https://doi.org/10.1155/2019/5687343.
  4. M. Aljuaid, F. Colonna, Composition Operators on Some Banach Spaces of Harmonic Mappings, J. Funct. Spaces. 2020 (2020), 9034387. https://doi.org/10.1155/2020/9034387.
  5. M. Aljuaid, F. Colonna, On the Harmonic Zygmund Spaces, Bull. Aust. Math. Soc. 101 (2020), 466–476. https://doi.org/10.1017/s0004972720000180.
  6. S. Axler, P. Bourdon, W. Ramey, Harmonic function theory, Springer, New York, 2001. https://doi.org/10.1007/978-1-4757-8137-3.
  7. 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.
  8. M.A. Bakhit, A. Kamal, On Stevic-Sharma Operators from General Class of Analytic Function Spaces into ZygmundType Spaces, J. Funct. Spaces. 2022 (2022), 6467750. https://doi.org/10.1155/2022/6467750.
  9. C. Boyd, P. Rueda, Isometries of Weighted Spaces of Harmonic Functions, Potent. Anal. 29 (2008), 37–48. https://doi.org/10.1007/s11118-008-9086-4.
  10. R.E. Castillo, J.C. Ramos-Fernández, E.M. Rojas, A New Essential Norm Estimate of Composition Operators from Weighted Bloch Space into µ-Bloch Spaces, J. Funct. Spaces. 2013 (2013), 817278. https://doi.org/10.1155/2013/817278.
  11. 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.
  12. F. Colonna, The Bloch Constant of Bounded Harmonic Mappings, Indiana Univ. Math. J. 38 (1989), 829–840. https://www.jstor.org/stable/24895370.
  13. C. Cowen, B. MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995.
  14. Y. Estaremi, A. Ebadian, S. Esmaeili, Essential norm of composition operators on Harmonic Bloch spaces, Filomat. 36 (2022), 3105–3118. https://doi.org/10.2298/fil2209105e.
  15. E. Jorda, A.M. Zarco, Isomorphisms on Weighed Banach Spaces of Harmonic and Holomorphic Functions, J. Funct. Spaces. 2013 (2013), 178460. https://doi.org/10.1155/2013/178460.
  16. E. Jorda, A.M. Zarco, Weighted Banach spaces of harmonic functions, Rev. R. Acad. Cienc. Exactas Fis. Nat., Ser. A Mat., RACSAM. 108 (2012), 405–418. https://doi.org/10.1007/s13398-012-0109-z.
  17. A. Kamal, S.A. Abd-Elhafeez, M. Hamza Eissa, On Product-Type Operators Between H ∞ and Zygmund Spaces, Appl. Math. Inf. Sci. 16 (2022), 623–633. https://doi.org/10.18576/amis/160416.
  18. J. Laitila, H.O. Tylli, Composition Operators on Vector-valued Harmonic Functions and Cauchy Transforms, Indiana Univ. Math. J. 55 (2006), 719–746. https://www.jstor.org/stable/24902369.
  19. W. Lusky, On Weighted Spaces of Harmonic and Holomorphic Functions, J. London Math. Soc. 51 (1995), 309– 320. https://doi.org/10.1112/jlms/51.2.309.
  20. W. Lusky, On the Isomorphism Classes of Weighted Spaces of Harmonic and Holomorphic Functions, Stud. Math. 175 (2006), 19–45. https://eudml.org/doc/285212.
  21. 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.
  22. C. Zhang, Compact Composition Operators on Besov Spaces on the Unit Ball, Bull. Korean Math. Soc. 60 (2023), 649–657. https://doi.org/10.4134/BKMS.B220137.