\overline∂_{𝑏}-equations on certain unbounded weakly pseudo-convex domains

Abstract

Abstract.We found an explicit closed formula for the relative fundamental solution of db on the surface Hk = {(z\, z2) € C2 : Im z2 = |zi|2*} ■ We then make estimates of the relative fundamental solution in terms of the nonisotropic metric associated with the surface. The estimates lead us to the regularity results. We also study the problem of finding weights w so that db as an operator from L2, to L1 has a closed range. We find the best possible weight among radial weights.