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Peer-reviewedCC BY 4.0Axioms

New Criteria for Composition Operators into Weighted Harmonic Bloch Spaces

  • Mahmoud Ali Bakhit1
  • Munirah Aljuaid2
  1. 1Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia
  2. 2Department of Mathematics, Northern Border University, Arar 73222, Saudi Arabia
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Abstract

In this paper, we obtain new criteria for the boundedness, the compactness and the essential norm of composition operators acting from the space H∞ of bounded harmonic mappings into weighted harmonic Bloch spaces BHα, 0<α<∞, on the unit disk. These criteria are expressed in terms of the asymptotic behavior of the sequence {∥Cψqk∥BHα}k≥0, where qk(z)=zk+z¯k, and of a family of test functions Fa,n normalized by Fa,n(a)=2. We further relate these quantities to an explicit function of the symbol ψ, which yields symbol-based characterizations of boundedness and compactness, and two-sided estimates with absolute constants for the essential norm of Cψ:H∞→BHα.

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Cite

BibTeXRIS
BibTeX
@article{bakhit2026criteria,
  title = {{New Criteria for Composition Operators into Weighted Harmonic Bloch Spaces}},
  author = {Mahmoud Ali Bakhit and Munirah Aljuaid},
  journal = {Axioms},
  year = {2026},
  month = oct,
  doi = {10.3390/axioms15100764},
  url = {https://www.mdpi.com/2075-1680/15/10/764},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - New Criteria for Composition Operators into Weighted Harmonic Bloch Spaces
AU  - Mahmoud Ali Bakhit
AU  - Munirah Aljuaid
PY  - 2026
DA  - 2026/10/13
JO  - Axioms
DO  - 10.3390/axioms15100764
UR  - https://www.mdpi.com/2075-1680/15/10/764
AB  - In this paper, we obtain new criteria for the boundedness, the compactness and the essential norm of composition operators acting from the space H∞ of bounded harmonic mappings into weighted harmonic Bloch spaces BHα, 0<α<∞, on the unit disk. These criteria are expressed in terms of the asymptotic behavior of the sequence {∥Cψqk∥BHα}k≥0, where qk(z)=zk+z¯k, and of a family of test functions Fa,n normalized by Fa,n(a)=2. We further relate these quantities to an explicit function of the symbol ψ, which yields symbol-based characterizations of boundedness and compactness, and two-sided estimates with absolute constants for the essential norm of Cψ:H∞→BHα.
SN  - 2075-1680
ER  -