Uniform estimates with weights for thebar partial - equation

This paper concernsL ^∞-variants of Hörmanders weightedL ²-estimates for the $bar partial - equation$ . In particular, we discuss a conjecture concerning suchL ^∞-estimates which is related to the corona problem in the ball, and show a weaker version of this conjecture. The proof uses a refinedL ²-estimate for the canonical solution to the $bar partial - equation$ . An alternative approach based on von Neumann’s Minimax theorem is also given.