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In this note we consider 
$\bar{\partial }$-problem in line bundles over complex projective space 
$\mathbb{C}{{\mathbb{P}}^{1}}$ and prove that the equation can be solved for (0, 1) forms with compact support. As a consequence, any Cauchy-Riemann function on a compact real hypersurface in such line bundles is a jump of two holomorphic functions defined on the sides of the hypersurface. In particular, the results can be applied to 
$\mathbb{C}{{\mathbb{P}}^{2}}$ since by removing a point from it we get a line bundle over $\mathbb{C}{{\mathbb{P}}^{1}}$.
