zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Calderón-Zygmund theory for non-integral operators and the H functional calculus. (English) Zbl 1057.42010

Summary: We modify Hörmander’s well-known weak type (1,1) condition for integral operators (in a weakened version due to Duong and McIntosh) and present a weak type (p,p) condition for arbitrary operators.

Given an operator A on L 2 with a bounded H calculus, we show as an application the L r -boundedness of the H calculus for all r(p,q), provided the semigroup (e -tA ) satisfies suitable weighted L p L q -norm estimates with 2(p,q).

This generalizes results due to Duong, McIntosh and Robinson for the special case (p,q)=(1,) where these weighted norm estimates are equivalent to Poisson-type heat kernel bounds for the semigroup (e -tA ). Their results fail to apply in many situations where our improvement is still applicable, e.g., if A is a Schrödinger operator with a singular potential, an elliptic higher-order operator with bounded measurable coefficients or an elliptic second-order operator with singular lower order terms.

42B20Singular and oscillatory integrals, several variables
47A60Functional calculus of operators
47F05Partial differential operators
42B25Maximal functions, Littlewood-Paley theory