Recently, by Z. Shen, resolvent estimates for the Stokes operator were established in *L*^{p}(Ω) when *Ω* is a Lipschitz domain in *R*^{d}, with *d≥3* and* |1/p-1/2|<1/(2d)+ε*. This result implies that the Stokes operator generates a bo
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Recently, by Z. Shen, resolvent estimates for the Stokes operator were established in *L*^{p}(Ω) when *Ω* is a Lipschitz domain in *R*^{d}, with *d≥3* and* |1/p-1/2|<1/(2d)+ε*. This result implies that the Stokes operator generates a bounded analytic semigroup in *L*^{p}(Ω) in the case that *Ω* is a three-dimensional Lipschitz domain and *3/2-ε<p<3+ε*. To fully understand the work of Z. Shen, a lot of background information is needed. In this thesis the resolvent estimates are studied in detail in the case *d=3*. In the end the results of Shen are extended to resolvent estimates in *L*^{p}(w,Ω), where *Ω* is a three-dimensional Lipschitz domain, *|1/p-1/2|<1/6*, and *w∈A*_{2p/3}∩RH_{3/(3-p)} is a weight function that belongs to an intersection of a Muckenhoupt weight class and satisfies a reverse Hölder inequality.