Generalized Weighted Composition Operator on Weighted Hardy Spaces - Pawan Kumar (International Journal of Mathematics And its Applications, 2026)
Let $φ$ be an analytic self-map of the open unit disc $\mathbb {D}$ in the finite complex plane $\mathbb{C}$ and $ψ$ be an analytic map of the open unit disc $\mathbb {D}$ to $\mathbb{C}$. Let $ C_{φ}\;,M_{ψ}\;and\;D^n $ be the composition, multiplication and differentiation operators defined by $C_{φ}f=f°φ,\; M_{ψ}f=ψ.f \;and\; D^{n}f= f^{n} $ respectively. In this paper, we shall study the boundedness and compactness of the generalized weighted composition operator $W_{ψ\;φ}D^{n}$ defined by $W_{ψ\;φ}D^{n}f\;=\;ψ.(f^{n}°φ)$ on weighted Hardy spaces by using the orthonormal basis of the weighted Hardy spaces $H^{2}(β)$.