Hardy type and more general weighted integral inequalites

 

Lars-Erik Persson

Department of Mathematics, Luleå University of Technology S-971 87 Luleå, SWEDEN


 First I present and discuss Hardy´s original inequality and some historical remarks concerning this inequality. After that I present some, in my opinon, important questions and developments up to the theory presented in the Opic-Kufner book [1]. I will also present some newer results concerning more general integral inequalities and my own picture of the state of art including some information we have collected and developed in [2]. I will also present some new results and thoughts concerning limiting inequalities of Carleman (Knopp -Carleson) type (see e.g. [3]). A number of open questions will be raised.

 

References

 

[1] B. Opic and A. Kufner, Hardy-type inequalities, Pitman Research Notes in Mathematics Series, Scientific & Technical, Harlow, 1990.

[2]  A. Kufner and L.E. Persson, Integral Inequalities with Weights, book manuscript, 2000.

[3] L.E. Persson and V. Stepanov, Weighted integral inequalities with the geometric mean operator, Doklady Mathematics 377 (2001).