  Translation of the paper "Interpolation of linear spaces and maximum
estimates for solutions to parabolic equations" published in Russian in the
collected volume "Partial differential equations", Akad. Nauk SSSR, Sibirsk.
Otdel., Inst. Mat., Novosibirsk, 1987, 50--72. Original proofs are essentially
simplified. Some gaps are fixed and some comments are added.
