Algebras of Singular Integral Operators with Kernels Controlled by Multiple Norms

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...

Celý popis

Uloženo v:
Podrobná bibliografie
Hlavní autoři: Nagel, Alexander, Ricci, Fulvio, Stein, Elias M., Wainger, Stephen
Médium: E-kniha Kniha
Jazyk:angličtina
Vydáno: Providence, Rhode Island American Mathematical Society 2018
Vydání:1
Edice:Memoirs of the American Mathematical Society
Témata:
Algebra
Integral operators
Kernel functions
Operator algebras
Singular integrals
Multiplier operators
Multi-parameter theory
Homogeneous nilpotent Lie groups
Flag kernels
Pseudo-differential operators
Singular integral operators
ISBN:9781470434380, 1470434385
ISSN:0065-9266, 1947-6221
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí: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.
Bibliografie:November 2018, volume 256, number 1230 (sixth of 6 numbers)
Includes bibliographical references (p. 139-140) and index
ISBN:9781470434380
1470434385
ISSN:0065-9266
1947-6221
DOI:10.1090/memo/1230