## Basic properties of Sobolev’s spaces on time scales.(English)Zbl 1139.39022

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

### MSC:

 39A12 Discrete version of topics in analysis 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems

### Keywords:

Sobolev spaces; time scale; Lebesgue $$\Delta$$-measure
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### References:

 [1] Bohner M, Peterson A (Eds): Advances in Dynamic Equations on Time Scales. Birkhäuser Boston, Massachusetts; 2003:xii+348. · Zbl 1025.34001 [2] Brezis H: Analyse Fonctionnelle: Thèorie et Applications. Masson, Paris; 1996. [3] Cabada, A; Vivero, DR, Criterions for absolute continuity on time scales, Journal of Difference Equations and Applications, 11, 1013-1028, (2005) · Zbl 1081.39011 [4] Cabada A, Vivero DR: Expression of the Lebesgue Δ-integral on time scales as a usual Lebesgue integral. Application to the calculus of Δ-antiderivatives. to appear in Mathematical and Computer Modelling · Zbl 1092.39017 [5] Guseinov, GSh, Integration on time scales, Journal of Mathematical Analysis and Applications, 285, 107-127, (2003) · Zbl 1039.26007 [6] Hewitt E, Stromberg K: Real and Abstract Analysis. A Modern Treatment of the Theory of Functions of a Real Variable, Graduate Texts in Mathematics, no. 25. 3rd edition. Springer, New York; 1975:x+476. · Zbl 0307.28001 [7] Rudin W: Real and Complex Analysis. 1st edition. McGraw-Hill, New York; 1966:xi+412. · Zbl 0142.01701 [8] Rudin W: Real and Complex Analysis. 3rd edition. McGraw-Hill, New York; 1987:xiv+416. · Zbl 0925.00005
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