Table of Contents Author Guidelines Submit a Manuscript
Journal of Function Spaces and Applications
Volume 3, Issue 3, Pages 287-320

Box dimension, oscillation and smoothness in function spaces

Departamento de Matemática of Universidade de Aveiro, 3810-193 Aveiro, Portugal

Received 1 October 2004

Academic Editor: Hans Triebel

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of this paper is twofold. First we relate upper and lower box dimensions with oscillation spaces, and we develop embeddings or inclusions between oscillation spaces and Besov spaces. Secondly, given a point in the (1p, s)-plane we determine maximal and minimal values for the upper box dimension (also the maximal value for lower box dimension) for the graphs of continuous real functions with a compact support, represented by this point.