Realization and characterization of modulus of smoothness in weighted lebesgue spaces

Abstract

A characterization is obtained for the modulus of smoothness in the Lebesgue spaces L-omega(p), 1 < p < infinity, with weights omega satisfying the Muckenhoupt A(p) condition. Also, a realization result and the equivalence between the modulus of smoothness and the Peetre K-functional are proved in L-omega(p) for 1 < p < infinity and omega is an element of A(p).