$$L^\infty $$ estimates for the Banach-valued $${{\bar{\partial }}}$$-problem in a disk

We study the differential equation $$\frac{\partial G}{\partial {{\bar{z}}}}=g$$ with an unbounded Banach-valued Bochner measurable function g on open unit disk $${\mathbb {D}}\subset {{\mathbb {C}}}$$ . prove that under some conditions growth and essential support of such has a bounded solution given by continuous linear operator. The obtained results are applicable to corona problem for algebra holomorphic functions {D}}$$ values in complex commutative unital Banach algebra.