Hardy-type inequalities

✍ Scribed by Opic P., Kufner A.

• Publisher: Pitman
• Year: 1990
• Tongue: English
• Leaves: 344
• Series: Pitman Research Notes in Mathematics Series
• Category: Library

✦ Synopsis

This provides a discussion of Hardy-type inequalities. They play an important role in various branches of analysis such as approximation theory, differential equations, theory of function spaces etc. The one-dimensional case is dealt with almost completely. Various approaches are described and some extensions are given (eg the case of estaimates involving higher order derivatives, or the dependence on the class of funcions for which the inequality should hold). The N-dimensional case is dealt with via the one-dimensional case as well as by using appropriate special approaches.

✦ Table of Contents

Title Page......Page 2
Copyright Page......Page 3
Contents......Page 4
Preface......Page 5
List of symbols......Page 6
Introduction......Page 12
1. Formulation of the problem......Page 16
2. Historical remarks......Page 25
3. Proofs of Theorems 1.14 and 1.15......Page 32
4. The method of differential equations......Page 46
5. The limit values of the exponents p , q......Page 56
6. Functions vanishing at the right endpoint. Examples......Page 76
7. Compactness of the operators H_L and H_R......Page 84
8. The Hardy inequality for functions from AC_{LR}(a,b)......Page 103
9. The Hardy inequality for 0 < q < 1......Page 140
10. Higher order derivatives......Page 153
11. Some remarks......Page 172
12. Introduction......Page 181
13. Some elementary methods......Page 197
14. The approach via differential equations and formulas......Page 215
15. The Hardy inequality and the class A_r......Page 237
16. Some special results......Page 246
17. Some general necessary and sufficient conditions......Page 254
18. Imbeddings for the case 1 < p < q < infty......Page 260
19. Power type weights......Page 280
20. Unbounded domains......Page 298
21. The N-dimensional Hardy inequality......Page 315
22. Level intervals and level functions......Page 326
References......Page 338