We present a weighted Lp-theory of parabolic systems on a half space Rd+. The leading coefficients are assumed to be only measurable in time t and have small bounded mean oscillations (BMO) with respect to the spatial variables x, and the lower order coefficients are allowed to blow up near the boundary.
2020 Mathematics Subject Classification. 35K51, 35R05. Key words and phrases. sharp/maximal functions, parabolic systems, weighted Sobolev spaces, measurable coefficients. The first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1A2C1084683).The second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1A2C1A01003354). The third author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2019R1F1A1058988). \u2217Corresponding author.
