Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
Share this page via the icons above, or by copying the link below:
Copy To Clipboard
Successfully Copied!
Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms
 
Alexander Nagel University of Wisconsin-Madison, WI
Fulvio Ricci Scuola Normale Superiore, Pisa, Italy
Elias M. Stein Princeton University, Princeton, NJ
Stephen Wainger University of Wisconsin-Madison, WI
Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms
eBook ISBN:  978-1-4704-4923-0
Product Code:  MEMO/256/1230.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms
Click above image for expanded view
Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms
Alexander Nagel University of Wisconsin-Madison, WI
Fulvio Ricci Scuola Normale Superiore, Pisa, Italy
Elias M. Stein Princeton University, Princeton, NJ
Stephen Wainger University of Wisconsin-Madison, WI
eBook ISBN:  978-1-4704-4923-0
Product Code:  MEMO/256/1230.E
List Price: $78.00
MAA Member Price: $70.20
AMS Member Price: $46.80
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2562018; 141 pp
    MSC: Primary 42; 35;

    The authors study algebras of singular integral operators on \(\mathbb R^n\) and nilpotent Lie groups that arise when considering the composition of Calderón-Zygmund operators with different homogeneities, such as operators occuring in sub-elliptic problems and those arising in elliptic problems. These algebras are characterized in a number of different but equivalent ways: in terms of kernel estimates and cancellation conditions, in terms of estimates of the symbol, and in terms of decompositions into dyadic sums of dilates of bump functions. The resulting operators are pseudo-local and bounded on \(L^p\) for \(1 \lt p \lt \infty \). While the usual class of Calderón-Zygmund operators is invariant under a one-parameter family of dilations, the operators studied here fall outside this class, and reflect a multi-parameter structure.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. The Classes $\mathcal P(\mathbf E)$ and $\mathcal M({\mathbf E})$
  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2562018; 141 pp
MSC: Primary 42; 35;

The authors study algebras of singular integral operators on \(\mathbb R^n\) and nilpotent Lie groups that arise when considering the composition of Calderón-Zygmund operators with different homogeneities, such as operators occuring in sub-elliptic problems and those arising in elliptic problems. These algebras are characterized in a number of different but equivalent ways: in terms of kernel estimates and cancellation conditions, in terms of estimates of the symbol, and in terms of decompositions into dyadic sums of dilates of bump functions. The resulting operators are pseudo-local and bounded on \(L^p\) for \(1 \lt p \lt \infty \). While the usual class of Calderón-Zygmund operators is invariant under a one-parameter family of dilations, the operators studied here fall outside this class, and reflect a multi-parameter structure.

  • Chapters
  • 1. Introduction
  • 2. The Classes $\mathcal P(\mathbf E)$ and $\mathcal M({\mathbf E})$
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.