Integral operators determined by quasielliptic equations. I

A family of integral operators is considered which appears in the construction of approximate solutions to quasielliptic equations on $R_n$. Properties of the operators are studied in the weighted Sobolev spaces $W_{p,\sigma}^r(R_n)$. The results obtained are applied to investigating solvability conditions for quasielliptic equations over $W_{p,\sigma}^r(R_n)$. A class of equations is indicated for which unconditional solvability holds.