Fundamental solutions of quasielliptic equations are constructed; this allo
ws the author to develop a relevant theory of volume potentials, establish
estimates for the Holder norms of solutions of equations with constant coef
ficients, and extend them after that to equations with variable coefficient
s. As a result, sharp Schauder-type interior estimates are obtained, of whi
ch the well-known classical results for elliptic and parabolic equations ar
e special cases.