Functions of Bounded kth p-Variation and Continuity Modulus

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 the...

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Bibliographic Details
Main Authors: Odalis Mejía, Pilar Silvestre
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2015/253636
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Summary: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.
ISSN:2314-8896
2314-8888