For $p$-solvable groups, a strong form of Alperin's weight conjecture has been proved by T. Okuyama (unpublished). L. Barker has refined this theorem by taking Green correspondence into account. We prove here a relative version of Barker's theorem.
Masafumi MURAI. "On Alperin's weight conjecture for $p$-blocks of $p$-solvable groups." J. Math. Soc. Japan 65 (4) 1037 - 1054, October, 2013. https://doi.org/10.2969/jmsj/06541037