This paper is concerned with the standard estimate of solutions to the resolvent problem for the Stokes operator on an infinite layer.
Takayuki ABE. Yoshihiro SHIBATA. "On a resolvent estimate of the Stokes equation on an infinite layer." J. Math. Soc. Japan 55 (2) 469 - 497, April, 2003. https://doi.org/10.2969/jmsj/1191419127