On the factorable strong $p$-nuclearity of Bloch maps

We introduce and study the concept of factorable strongly $p$-nuclear Bloch maps, a novel class of mappings in the category of Bloch functions. We provide several characterizations of these maps, including a Pietsch-type domination theorem and connections to $p$-nuclear linear operators via their linearization and transposition. Key properties such as Möbius invariance and duality by applying the theory on tensor products are established. We also investigate the injective Banach ideal structure of these maps and their Bloch weak compactness properties. The results extend known theory on Bloch mappings, offering new insights into their interplay.