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)
Norm-attaining integral operators on analytic function spaces. (English) Zbl 1257.30061

Summary: If f and g are analytic functions in the unit disc 𝔻, we define

S g (f)(z)= 0 z f ' (w)g(w)dw,z𝔻·

If g is bounded, then the integral operator S g is bounded on the Bloch space, on the Dirichlet space, and on BMOA. We show that S g is norm-attaining on the Bloch space and on BMOA for any bounded analytic function g, but does not attain its norm on the Dirichlet space for non-constant g. Some results are also obtained for S g on the little Bloch space, and for another integral operator T g from the Dirichlet space to the Bergman space.

MSC:
30H20Bergman spaces, Fock spaces
30H30Bloch spaces
30H35BMO-spaces
47A30Operator norms and inequalities
47A10Spectrum and resolvent of linear operators