Hardy and Littlewood Inequalities on Time Scales

S. H. Saker1, Donal O’Regan2
1Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt
2School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland

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Tài liệu tham khảo

Agarwal, R.P., Bohner, M., O’Regan, D., Saker, S.H.: Some Wirtinger-type inequalities on time scales and their applications. Pacific J. Math. 252, 1–26 (2011)

Bohner, M., Peterson, A.: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser, Boston (2001)

Bohner, M., Peterson, A.: Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston (2003)

Chan, L.Y.: Some extensions of Hardy’s inequality. Can. Math. Bull. 22, 165–169 (1979)

Chen, D.-X.: Bounded oscillation of second-order half-linear neutral delay dynamic equations. Bull. Malays. Math. Sci. Soc. (2) 36(3), 807–823 (2013)

Elliott, E.B.: A simple expansion of some recently proved facts as to convergency. J. Lond. Math. Soc. 1, 93–96 (1926)

Hardy, G.H.: Notes on a theorem of Hilbert. Math. Z. 6, 314–317 (1920)

Hardy, G.H., Littlewood, J.E.: Elementary theorems concerning power series with positive coefficients and moment constants of positive functions. J. Reine Angew Math. 157, 141–158 (1927)

Hardy, G.H.: Notes on some points in the integral calculus. Messenger Math. 57, 12–16 (1928)

Hilger, S.: Analysis on measure chains –a unified approach to continuous and discrete calculus. Results Math. 18, 18–56 (1990)

Hu, M., Xie, P., Wang, L.: Almost periodic solutions of neutral delay functional differential equations on time scales. Bull. Malays. Math. Sci. Soc. 38, 317–331 (2015)

Izumi, M., Izumi, S.: On some inequalities for Fourier series. J. D’Analyse Math. 21, 277–291 (1968)

Kaijser, S., Persson, L.E., Öberg, A.: On Carleman and Knopp’s inequalities. J. Approx. Theor. 117, 140–151 (2002)

Kufner, A., Persson, Lars-Erik: Weighted Inequalities of Hardy Type. World Scientific Publishing, Singapore (2003)

Kufner, A., Maligranda, L., Persson, L.: The Hardy inequalities: About its History and Some Related Results. Vydavatelský servis, Pilsen (2007)

Levinson, N.: Generalizations of an inequality of Hardy. Duke Math. J. 31, 389–394 (1964)

Németh, J.: Generalizations of the Hardy-Littlewood inequality. II. Acta Sci. Math. 35, 127–134 (1973)

Oguntuase, J.A., Imoru, C.O.: New generalizations of Hardy’s integral inequalities. J. Math. Anal. Appl. 241, 73–82 (2000)

Oguntuase, J.A., Adeleke, E.O.: On Hardy’s integral inequality. Facta Univ. (NIS), Ser. Math. Infor. 20, 9–20 (2005)

Opic, B., Kufner, A.: Hardy-type Inequalities. Longman Scientific & Technical, Harlow (1989)

Ozkan, U.M., Yildirim, H.: Hardy-Knopp-type inequalities on time scales. Dyn. Sys. Appl. 17, 477–486 (2008)

Pachpatte, B.G.: A note on certain inequalities related to Hardy’s inequality. Indian J. Pure Appl. Math 23, 773–776 (1992)

Řehak, P.: Hardy inequality on time scales and its application to half-linear dynamic equations. J. Ineq. Appl. 2005(5), 495–507 (2005)

Saker, S.H.: Oscillation Theory of Dynamic Equations on Time Scales: Second and Third Orders. Lambert Academic Publishing, Germany (2010)

Sidi Ammi, M.R., Torres, D.F.M.: Hölder’s and Hardy’s two dimensional diamond-alpha inequalities on time scales. Ann. Univ. Craiova, Math. Comp. Ser. 37, 1–11 (2010)

Tongxing, L., Zhenlai, H., Shurong, S., Yige, Z.: Oscillation results for third order nonlinear delay dynamic equations on time scales. Bull. Malays. Math. Sci. Soc. (2) 34(3), 639–648 (2011)

Tuna, A., Kutukcu, S.: Some integrals inequalities on time scales. Appl. Math. Mech. Eng. Ed. 29, 23–29 (2008)

Wang, A., Yang, B.: On the reverse Hardy-Littlewood’s inequality. Inter. Math. Forum 7, 241–249 (2012)

Zhang, C., Agarwal, R.P., Bohner, M., Li, T.: Oscillation of second-order nonlinear neutral dynamic equations with noncanonical operators. Bull. Malays. Math. Sci. Soc. 38(2), 761–778 (2015)