This paper provides a careful and accessible exposition of the theory of analytic semigroups which may have weak singularity at the origin, with emphasis on its applications to a class of subelliptic initial-boundary value problems for linear parabolic differential equations of second order.
"The theory of semigroups with weak singularity and its applications to partial differential equations." Tsukuba J. Math. 13 (2) 513 - 562, December 1989. https://doi.org/10.21099/tkbjm/1496161173