Introduction; 1. Measure and integral; 2. The Cauchy–Schwarz inequality; 3. The AM-GM inequality; 4. Convexity, and Jensen's inequality; 5. The Lp spaces; 6. Banach function spaces; 7. Rearrangements; 8. Maximal inequalities; 9. Complex interpolation; 10. Real interpolation; 11. The Hilbert transform, and Hilbert's inequalities; 12. Khintchine's inequality; 13. Hypercontractive and logarithmic Sobolev inequalities; 14. Hadamard's inequality; 15. Hilbert space operator inequalities; 16. Summing operators; 17. Approximation numbers and eigenvalues; 18. Grothendieck's inequality, type and cotype.
This book contains a wealth of inequalities used in linear analysis, explaining in detail how they are used.
D. J. H. Garling is an Emeritus Reader in Mathematical Analysis at the University of Cambridge and a Fellow of St John's College, Cambridge.
'… contains a wealth of inequalities … both classical and contemporary, complemented with detailed recipes on how to use them. … The author … brings back Muirhead's maximal function, which is usually treated as a misnomer quoted to other authors. This book is a compulsory item on every teacher's bookshelf and it should be strongly recommended to students. … an endless source of very good problems for students' theses of all levels.' EMS Newsletter
 |
Ask a Question About this Product More... |
|
