TY - BOOK
AU - Citti,Giovanna
AU - Grafakos,Loukas
AU - Pérez,Carlos
AU - Sarti,Alessandro
AU - Zhong,Xiao
ED - SpringerLink (Online service)
TI - Harmonic and Geometric Analysis
T2 - Advanced Courses in Mathematics - CRM Barcelona,
SN - 9783034804080
AV - QA299.6-433
U1 - 515 23
PY - 2015///
CY - Basel
PB - Springer Basel, Imprint: Birkhäuser
KW - Mathematics
KW - Mathematical analysis
KW - Analysis (Mathematics)
KW - Partial differential equations
KW - Analysis
KW - Partial Differential Equations
N1 - 1 Models of the Visual Cortex in Lie Groups -- 2 Multilinear Calderón–Zygmund Singular Integrals -- 3 Singular Integrals and Weights -- 4 De Giorgi–Nash–Moser Theory
N2 - 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 Calderón–Zygmund theory, especially the Lp inequalities for Calderón–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
UR - http://dx.doi.org/10.1007/978-3-0348-0408-0
ER -