Advances in Difference Equations 
Volume 2006 (2006), Article ID 38121, 14 pages
doi:10.1155/ADE/2006/38121

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

Abstract

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.