Giovanna Citti, Loukas Grafakos, Carlos Pe+{327́}rez, Alessandro Sarti, Xiao Zhong ; editor for this volume: Joan Mateu
مشخصات ظاهری
نام خاص و کميت اثر
1 online resource (ix, 170 pages) :
ساير جزييات
illustrations (some color).
فروست
عنوان فروست
Advanced Courses in Mathematics - CRM Barcelona,
شاپا ي ISSN فروست
2297-0304
یادداشتهای مربوط به کتابنامه ، واژه نامه و نمایه های داخل اثر
متن يادداشت
Includes bibliographical references
یادداشتهای مربوط به مندرجات
متن يادداشت
1 Models of the Visual Cortex in Lie Groups -- 2 Multilinear Caldero+{327́}n Zygmund Singular Integrals -- 3 Singular Integrals and Weights -- 4 De Giorgi?Nash?Moser Theory
بدون عنوان
0
یادداشتهای مربوط به خلاصه یا چکیده
متن يادداشت
This book presents an expanded version of four series of lectures delivered by the authors at the CRM. Harmonic analysis, understood in a broad sense, has a very wide interplay with partial differential equations and in particular with the theory of quasiconformal mappings and its applications. Some areas in which real analysis has been extremely influential are PDE's and geometric analysis. Their foundations and subsequent developments made extensive use of the Caldero+{327́}n Zygmund theory, especially the Lp inequalities for Caldero+{327́}n Zygmund operators (Beurling transform and Riesz transform, among others) and the theory of Muckenhoupt weights. The first chapter is an application of harmonic analysis and the Heisenberg group to understanding human vision, while the second and third chapters cover some of the main topics on linear and multilinear harmonic analysis. The last serves as a comprehensive introduction to a deep result from De Giorgi, Moser and Nash on the regularity of elliptic partial differential equations in divergence form