Jackson and Inverse inequalities in rearrangement invariant banach function spaces on dini-smooth domains

Abstract

In this work we obtain some Jackson type direct theorem and converse theorem of polynomial approximation with respect to fractional order moduli of smoothness in rearrangement invariant quasi Banach function spaces (RIQBFS) on the unit circle. Later using these results we obtain similar estimates for some RIBFS on sufficiently smooth domains of complex plane.