  The present paper concerns filtered de la Vall\'ee Poussin (VP) interpolation
at the Chebyshev nodes of the four kinds. This approximation model is
interesting for applications because it combines the advantages of the
classical Lagrange polynomial approximation (interpolation and polynomial
preserving) with the ones of filtered approximation (uniform boundedness of the
Lebesgue constants and reduction of the Gibbs phenomenon). Here we focus on
some additional features that are useful in the applications of filtered VP
interpolation. In particular, we analyze the simultaneous approximation
provided by the derivatives of the VP interpolation polynomials. Moreover, we
state the uniform boundedness of VP approximation operators in some Sobolev and
H\"older--Zygmund spaces where several integro--differential models are
uniquely and stably solvable.
