Functions of Bounded kth p-Variation and Continuity Modulus - Odalis Mejía; Pilar Silvestre (Journal of Function Spaces)
A scale of spaces exists connecting the class of functions of bounded kth p-variation in the sense of Riesz-Merentes with the Sobolev space of functions with p-integrable kth 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 order k-1/p.