On the Norm of Certain Weighted Composition Operators on the Hardy Space

Abstract

We obtain a representation for the norm of certain compact weighted composition operator $C_{\psi ,\phi }$ on the Hardy space $H^2$, whenever $\phi \left(z\right)=az+b$ and $\psi \left(z\right)=az-b$. We also estimate the norm and essential norm of a class of noncompact weighted composition operators under certain conditions on $\phi$ and $\psi$. Moreover, we characterize the norm and essential norm of such operators in a special case.