Let
M
\mathcal M
be a smooth real hypersurface in complex space of dimension
n
≥
3
n\ge 3
, and assume that the Levi-form at
z
0
z_0
on
M
\mathcal M
has at least two positive eigenvalues. We estimate solutions of the local
∂
¯
\bar {\partial }
-closed extension problem near
z
0
z_0
for
(
0
,
1
)
(0,1)
-forms in Sobolev spaces. Using this result, we estimate the local solution of tangential Cauchy-Riemann equations near
z
0
z_0
for
(
0
,
1
)
(0,1)
-forms in Sobolev spaces.