We review the proof of regularty of weak solutions for heat equations and then consider a class of ultraparabolic differential equations with measurable coefficients and lower order terms.  It is proved that weak solutions to the equation are Holder continuous,which generalizes the classic results of parabolic equations with general coefficients. The main observation is a weak Sobolev inequality and Poincare inequality related to weak sub-solutions. This is a jointed work with Wang Wendong.