Inequalities: A Journey into Linear Analysis
$79.99 (P)
- Author: D. J. H. Garling, St John's College, Cambridge
- Date Published: July 2007
- availability: Available
- format: Paperback
- isbn: 9780521699730
$
79.99
(P)
Paperback
Other available formats:
Hardback, eBook
Looking for an examination copy?
This title is not currently available for examination. However, if you are interested in the title for your course we can consider offering an examination copy. To register your interest please contact collegesales@cambridge.org providing details of the course you are teaching.
-
This book contains a wealth of inequalities used in linear analysis, and explains in detail how they are used. The book begins with Cauchy's inequality and ends with Grothendieck's inequality, in between one finds the Loomis-Whitney inequality, maximal inequalities, inequalities of Hardy and of Hilbert, hypercontractive and logarithmic Sobolev inequalities, Beckner's inequality, and many, many more. The inequalities are used to obtain properties of function spaces, linear operators between them, and of special classes of operators such as absolutely summing operators. This textbook complements and fills out standard treatments, providing many diverse applications: for example, the Lebesgue decomposition theorem and the Lebesgue density theorem, the Hilbert transform and other singular integral operators, the martingale convergence theorem, eigenvalue distributions, Lidskii's trace formula, Mercer's theorem and Littlewood's 4/3 theorem. It will broaden the knowledge of postgraduate and research students, and should also appeal to their teachers, and all who work in linear analysis.
Read more- Establishes the fundamental inequalities of linear analysis
- Explains in detail how these important inequalities are used
- Provides breadth to courses on linear analysis
Reviews & endorsements
"This book combines the best features of a reference work and an organic development with unifying themes."
D.V. Feldman, University of New Hampshire for CHOICESee more reviews"I recommend this book to people who want to learn more about linear analysis, in particular, on harmonic analysis, Banach space techniques and operator theory, but also in several related aspects in probability theory." - Mark C. Veraar, Mathematical Reviews
Customer reviews
Not yet reviewed
Be the first to review
Review was not posted due to profanity
×Product details
- Date Published: July 2007
- format: Paperback
- isbn: 9780521699730
- length: 346 pages
- dimensions: 244 x 173 x 18 mm
- weight: 0.59kg
- contains: 128 exercises
- availability: Available
Table of Contents
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.-
Resources for
Inequalities: A Journey into Linear Analysis
D. J. H. Garling
General Resources
Find resources associated with this title
Type Name Unlocked * Format Size Showing of
This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to instructors whose faculty status has been verified. To gain access to locked resources, instructors should sign in to or register for a Cambridge user account.
Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other instructors may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.
Supplementary resources are subject to copyright. Instructors are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.
If you are having problems accessing these resources please contact lecturers@cambridge.org.
Related Books
related journals
also by this author
Sorry, this resource is locked
Please register or sign in to request access. If you are having problems accessing these resources please email lecturers@cambridge.org
Register Sign in» Proceed
You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner www.ebooks.com. Please see the permission section of the www.ebooks.com catalogue page for details of the print & copy limits on our eBooks.
Continue ×Are you sure you want to delete your account?
This cannot be undone.
Thank you for your feedback which will help us improve our service.
If you requested a response, we will make sure to get back to you shortly.
×