HARDY-SOBOLEV-MAZYA INEQUALITY FOR NABLA TIME SCALE CALCULUS

Yıl 2019, , 133 - 145, 23.08.2019

Neslihan Nesliye Pelen

https://doi.org/10.20290/estubtdb.609525

Cited By: 2

Öz

First
part of the study is mainly about some missing concepts of the measure theory
of nabla time scale calculus. In the second part, as an application of the
nabla measure theory, especially the nabla Sobolev spaces, Hardy- Sobolev Mazya
Inequality on nabla time scale is obtained and given.

Anahtar Kelimeler

Time scale calculus, Measure theory, Dynamic inequalities

Kaynakça

• Deniz A. Measure theory on time scales. MSc, Graduate School of Engineering and Sciences of Izmir Institute of Technology, Turkey, 2007. Cabada A and Vivero D. Expression of the Lebesgue Δ-Integral on Time Scales as a Usual Lebesgue Intregral; Application to the Calculus of Δ-Antiderivatives, Elsevier 4, 2004. pp.291-310. Guseinov SG. Integration on Time Scales, Elsevier Academic Press, No. 285, 2003. pp. 107-127. Hilger S: Analysis on measure chains - a unified approach to continuous and discrete calculus. Results Math. 1990. 18, 18-56. Roussas GG. An Introduction to Measure Theoretic Probability, Elsevier Academic Press, California, 2004. Bohner M and Peterson A. Dynamic Equations on Time Scales; An Introduction with Applications, Birkhauser, Boston, 2001. Rudin W. Real and Complex Analysis, McGraw-Hill, New York, 1987. Ferreira RAC, Ammi MRS, Torres DFM, Diamond-alpha Integral Inequalities on Time Scales Int. J. Math.Stat.5(A09), 2009, 52–59. Ozkan UM, Sarikaya MZ, Yildirim H. Extensions of certain integral inequalities on time scales, Appl. Math. Lett. 2008, 21 (10), 993-1000. Williams PA. Fractional Calculus on Time Scales with Taylor’s Theorem Fract. Calc. Appl. Anal. 2012, 15, 4. Guvenilir AF, Kaymakcalan B, Pelen NN. Constantin’s inequality for nabla and diamond-alpha derivative, J. Inequal. Appl. 2015, 2015:167.