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We study a division problem in the Hardy classes of the unit ball of which generalizes the corona problem, the generators being allowed to have common zeros. MPrecisely, if S is a subset of , we study conditions on a -valued bounded Mholomorphic function B, with , in order that for 1 ≤ p < ∞ and any function with there is a -valued holomorphic function F with f = B·F, i.e. the module generated by the components of B in the Hardy class is the entire module . As a special case,...
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