Remarks on the maximal regularity for parabolic boundary value problems with inhomogeneous data

Inspired by Ogawa-Shimizu [JEE 2022] and Chen-Liang-Tsai [IMRN 2025] on the second and first order derivative estimates of solution of heat equation in the upper half space with boundary data in homogeneous Besov spaces, we extend the estimates to any order of derivatives, including fractional derivatives.