We generalize a theorem of Freud and Szabados  on one-sided polynomial approxi- mation in five different directions: we allow functions with exponential growth at infinity, Lp-metric, Freud-type weights instead of Hermite weights, functions with bounded deriva- tives instead of bounded variation, and include the momentum in the error estimate.
In order to approximate functions defined on the real line or on the real semiaxis by polynomials, we introduce some new Fourier-type
operators, connected to the Fourier sums of generalized Freud or Laguerre orthonormal systems. We prove necessary and sufficient
conditions for the boundedness of these operators in suitable weighted Lp-spaces, with 1 < p < ∞. Moreover, we give error estimates in weighted Lp and uniform norms.
We generalize Laguerre weights on R+ by multiplying them by translations of finitely many Freud type weights which have singularities, and prove polynomial approximation
theorems in the corresponding weighted spaces.