zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Commutators of BMO functions and singular integral operators with non-smooth kernels. (English) Zbl 1023.42010
Summary: Let 𝒳 be a space of homogeneous type of infinite measure. Let T be a singular integral operator which is bounded on L p (𝒳) for some p, 1<p<. We give a sufficient condition on the kernel of T so that if a function bBMO(𝒳), then the commutator [b,T]=T(bf)-bT(f) is bounded on L p spaces for all p, 1<p<. Our condition is weaker than the usual Hörmander condition. Application include L p -boundedness of the commutators of BMO functions and holomorphic functional calculi of Schrödinger operators, and divergence form operators on irregular domains.

MSC:
42B20Singular and oscillatory integrals, several variables
47G10Integral operators
43A85Analysis on homogeneous spaces