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In trying to improve Weinstock's results on approximationby holomorphic functions on certain product domains, weare led to estimates in Sobolev spaces for the ∂¯-operator on polycylinders for (γ,q)-forms.This generalizes our results for the same operator onpolycylinders previously obtained, and can be applied to a numberof other problems such as the Corona problem

international journal of mathematics and mathematical sciences

Sobolev space estimates for solutions of the equation<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="${\overline{\partial}u} =f$"><mml:mrow><mml:mover accent="true"><mml:mo>∂</mml:mo><mml:mo>¯</mml:mo></mml:mover><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mi>f</mml:mi></mml:mrow></mml:math>on polycylinders

Sobolev space estimates for solutions of the equation∂¯u=fon polycylinders