  We show that the Peetre $K$-functional between the space $L_p$ with $0<p<1$
and the corresponding smooth function space $W_p^\psi$ generated by the
Weyl-type differential operator $\psi(D)$, where $\psi$ is a homogeneous
function of any positive order, is identically zero. The proof of the main
results is based on the properties of the de la Vall\'ee Poussin kernels and
the quadrature formulas for trigonometric polynomials and entire functions of
exponential type.
