Essential Norm of Composition Operators on Harmonic Zygmund Spaces and Their Derivative Spaces

Let ψ represent the analytic self-mapping within the unit disk D. We define the composition operator Cψ as Cψf = f◦ψ for every f belonging to the space of harmonic functions H(D). The essential norm of composition operators within specific harmonic mapping spaces is investigated in this research. Explicitly, we outline the essential norm of composition operators on the harmonic Zygmund spaces ZH and the derivative of harmonic Zygmund spaces VH. Notably, these results extend and build upon results that were established previously for the analytic settings.