On semiclassical orthogonal polynomials via polynomial mappings

We consider orthogonal polynomials via polynomial mappings in the framework of the semiclassical class. We prove that this class is stable under polynomial transformations. Several consequences of this fact are deduced. As an application we analyze in detail cubic transformations for semiclassical orthogonal polynomials of class at most 2, recovering and extending some results proved recently for class 1, and producing new examples of semiclassical orthogonal polynomials of class 2. In particular, we show how to obtain integral representations for the regular functionals with respect to which these new semiclassical families are orthogonal.