Norm Inequalities for Derivatives and Differences

Title page
Preface
Introduction
1 Unit Weight Functions
1.1 The Norms of y and y^(n)
1.2 The Norms of y, y^(k), and y^(n)
1.3 Inequalities of Product Form
1.4 Growth at Infinity
1.5 Notes and Problems
2 The Norms of y, y', y"
2.1 Introduction
2.2 The L^∞ Case
2.3 The L² Case
2.4 Equivalent Bounded Interval Problems for R
2.5 Equivalent Bounded Interval Problems for R+
2.6 The L¹ Case
2.7 Upper and Lower Bounds for k(p,R) and k(p,R+)
2.8 Extremals
2.9 Continuity as a Function of p
2.10 Landau's Inequality for Nondifferentiable Functions
2.11 Notes and Problems
3 Weights
3.1 Inequalities of the Sum Form
3.2 Inequalities of Product Form
3.3 Monotone Weight Functions
3.4 Positive Weight Functions
3.5 Weights with Zeros
3.6 Notes and Problems
4 The Difference Operator
4.1 The Discrete Product Inequality
4.2 The Second Order Case
4.3 Extremals
4.4 Notes and Problems
References
Subject Index