Functions of Boundedkthp-Variation and Continuity Modulus

Abstract

A scale of spaces exists connecting the class of functions of boundedkthp-variation in the sense of Riesz-Merentes with the Sobolev space of functions withp-integrablekth derivative. This scale is generated by the generalized functionals of Merentes type. We prove some limiting relations for these functionals as well as sharp estimates in terms of the fractional modulus of smoothness of orderk-1/p.