$(p,\theta ,q,\eta )$-Nuclear Bloch maps

Abstract

In this paper, new developments in the theory of ideals of Bloch maps are utilized to introduce and analyze the properties of $\left(p,\theta,q,\eta\right)$-nuclear Bloch maps from the open unit disk $\mathbb{D}$ to a complex Banach space $X,$ where $1\leq p,q<\infty $ and $0\leq \theta ,\eta<1$ satisfy $\left( 1-\theta \right) /p+\left( 1-\eta \right) /q=1$. The main emphasis is placed on defining these maps, establishing their Banach space properties, and investigating fundamental characteristics such as Pietsch domination, Bloch compactness and Möbius invariance. Finally, we conclude the paper by presenting a Bloch reasonable crossnorm and illustrating the isometric isomorphism between the defined space and its dual space.