Advances in Difference Equations
Volume 2006 (2006), Article ID 38121, 14 pages

Basic properties of Sobolev's spaces on time scales

Ravi P. Agarwal,1 Victoria Otero–Espinar,2 Kanishka Perera,1 and Dolores R. Vivero2

1Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901, FL, USA
2Departamento de Análise Matemática, Facultade de Matemáticas, Universidade de Santiago de Compostela, Santiago de Compostela 15782, Galicia, Spain

Received 18 January 2006; Accepted 22 January 2006

Copyright © 2006 Ravi P. Agarwal et al. 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.


We study the theory of Sobolev's spaces of functions defined on a closed subinterval of an arbitrary time scale endowed with the Lebesgue Δ-measure; analogous properties to that valid for Sobolev's spaces of functions defined on an arbitrary open interval of the real numbers are derived.