Resumen de Weighted γ-K-functional and γ-modulus of smoothness on the semiaxis
In this paper we investigate the γ-relative differentiation with the motivation of amending the order of the weighted polynomial approximation on the semiaxis for certain functions. By means of these tools, we give some definitions of generalized Sobolev spaces, K-functionals and moduli of smoothness. We estimate every one in terms of the others and, in the case of first order, we prove the equivalence. We show some possible applications and also other generalizations.
