  The Zakharov system in dimension $d\leqslant 3$ is shown to be locally
well-posed in Sobolev spaces $H^s \times H^l$, extending the previously known
result. We construct new solution spaces by modifying the $X^{s,b}$ spaces,
specifically by introducing temporal weights. We use contraction mapping
principle to prove local well-posedness in the same. The result obtained is
sharp up to endpoints.
