  Conditions for linear integral operators on $L_p$ over measure spaces to
satisfy the polynomial covariance type commutation relations are described in
terms of defining kernels of the corresponding integral operators.
Representation by integral operators are studied both for general polynomial
covariance commutation relations and for important classes of polynomial
covariance commutation relations associated to arbitrary monomials and to
affine functions. Representations of the covariance type commutation relations
by integral Volterra operators and integral convolution operators are
investigated.
