On Some Integral Inequalities Related to Hardy's

Christopher Olutunde Imoru

doi:10.4153/CMB-1977-047-6

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We obtain mainly by using Jensen's inequality for convex functions an integral inequality, which contains as a special case Shun's generalization of Hardy's inequality.

References

1. Boas, R. P. Jr; Integrability Theorems for Trigonometric Transforms. Ergebnisse der Mathematik und ihrer Grenzgebiete, Vol. 38, (1967).Google Scholar

2. Boas, R. P. Jr; Some Integral Inequalities Related to Hardy's Inequality. Journal d'analyse Math. 23 (1970), 53-63.Google Scholar

3. Hardy, G. H., Littlewood, J. E. and Pόlya, G: Inequalities. Second edition, Cambridge (1952).Google Scholar

4. Izumi, M, Izumi, S. and Peterson, G: On Hardy's inequality and its Generalizations. Tohoku Math. J. 21 (1969) 601-613.Google Scholar

5. Németh, J: Generalizations of Hardy-Littlewood Inequality 11. Acta Sci. Math. 32 (1971), 295-299.Google Scholar

6. Shum, D. T: On Integral Inequalities Related to Hardy's. Can. Math. Bull. 14 (2) (1971), 225-230.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Chan, Ling-Yau 1981. Some Further Extensions of Hardy's Inequality. Canadian Mathematical Bulletin, Vol. 24, Issue. 4, p. 393.

Pachpatte, B.G. 1987. On a new class of Hardy type inequalities. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 105, Issue. 1, p. 265.

Pachpatte, B.G 1987. On some variants of Hardy's inequality. Journal of Mathematical Analysis and Applications, Vol. 124, Issue. 2, p. 495.

Mitrinović, D. S. Pečarić, J. E. and Fink, A. M. 1991. Inequalities Involving Functions and Their Integrals and Derivatives. p. 143.

1992. Convex Functions, Partial Orderings, and Statistical Applications. Vol. 187, Issue. , p. 419.

Cheung, Wing-Sum Hanjš, Željko and Pečarić, Josip 2000. Some Hardy-Type Inequalities. Journal of Mathematical Analysis and Applications, Vol. 250, Issue. 2, p. 621.

2005. Mathematical Inequalities. Vol. 67, Issue. , p. 485.

2005. Mathematical Inequalities. Vol. 67, Issue. , p. 565.

Oguntuase, James Adedayo and Persson, Lars-Erik 2008. Refinement of Hardy's inequalities via superquadratic and subquadratic functions. Journal of Mathematical Analysis and Applications, Vol. 339, Issue. 2, p. 1305.

Abramovich, Shoshana Krulić, Kristina Pečarić, Josip and Persson, Lars-Erik 2010. Some new refined Hardy type inequalities with general kernels and measures. Aequationes mathematicae, Vol. 79, Issue. 1-2, p. 157.

Tian, Jingfeng and Zhou, Yang-Xiu 2013. Refinements of Hardy-Type Inequalities. Abstract and Applied Analysis, Vol. 2013, Issue. , p. 1.

Abramovich, S. and Persson, L.-E. 2014. Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Vol. 236, Issue. , p. 1.

Oguntuase, James A Fabelurin, Olanrewaju O Adeagbo-Sheikh, Abdulaziz G and Persson, Lars-Erik 2015. Time scale Hardy-type inequalities with ‘broken’ exponent p. Journal of Inequalities and Applications, Vol. 2015, Issue. 1,

Agarwal, Ravi P. O’Regan, Donal and Saker, Samir H. 2016. Hardy Type Inequalities on Time Scales. p. 221.

Fiorenza, Alberto and Jain, Pankaj 2021. A family of equivalent norms for Lebesgue spaces. Archiv der Mathematik, Vol. 116, Issue. 2, p. 179.

Article contents

On Some Integral Inequalities Related to Hardy's

Abstract

References

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests