Hardy’s Inequality on Time Scale
Main Article Content
Abstract
This work is concerned with the Hardy inequalityon time scales. It finds the condition for the existence of a constant C such that
where p is a fixed number satisfying .
Keywords:
Hardy inequality, time scales, exponential function.
References
[1] B. G. Pachpatte, Mathematical Inequalities, British Library Cataloguing in Publication Data, 2005.
[2] M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkh¨auser, Boston, 2001.
[3] B. Muckenhoupt, Hardy’s Inequality with Weights, Studia Math., Vol. 44, 1972, pp. 31-38, https://bibliotekanauki.pl/articles/1388490.
[4] Gusein Sh. Guseinov, Integration on Time Scales, J. Math. Anal. Appl., Vol. 285, 2003, pp. 107-127, https://doi.org/10.1016/S0022-247X(03)00361-5.
[5] E. A. Bohner, M. Bohner, F. Akin, Pachpatte Inequalities on Time Scales, J. Inequal. Pure Appl.
Math., Vol. 6, 2005, No.1, pp. 45-72, http://eudmd.org/doc/125938.
[6] N. H. Du, L. H. Tien, on the Exponential Stability of Dynamic Equations on Time Scales. J. Math. Anal.
Appl., Vol. 331, 2007, pp. 1159-1174, http://doi.org/10.1016/j.jmaa.2006.09.033.
[2] M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkh¨auser, Boston, 2001.
[3] B. Muckenhoupt, Hardy’s Inequality with Weights, Studia Math., Vol. 44, 1972, pp. 31-38, https://bibliotekanauki.pl/articles/1388490.
[4] Gusein Sh. Guseinov, Integration on Time Scales, J. Math. Anal. Appl., Vol. 285, 2003, pp. 107-127, https://doi.org/10.1016/S0022-247X(03)00361-5.
[5] E. A. Bohner, M. Bohner, F. Akin, Pachpatte Inequalities on Time Scales, J. Inequal. Pure Appl.
Math., Vol. 6, 2005, No.1, pp. 45-72, http://eudmd.org/doc/125938.
[6] N. H. Du, L. H. Tien, on the Exponential Stability of Dynamic Equations on Time Scales. J. Math. Anal.
Appl., Vol. 331, 2007, pp. 1159-1174, http://doi.org/10.1016/j.jmaa.2006.09.033.