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)
Compact composition operators on the Bloch space. (English) Zbl 0826.47023
Summary: Necessary and sufficient conditions are given for a composition operator C φ f=fφ to be compact on the Bloch space and on the little Bloch space 0 . Weakly compact composition operators on 0 are shown to be compact. If φ 0 is a conformal mapping of the unit disk 𝔻 into itself whose image φ(𝔻) approaches the unit circle 𝕋 only in a finite number of nontangential cusps, then C φ is compact on 0 . On the other hand if there is a point of 𝕋φ(𝔻) ¯ at which φ(𝔻) does not have a cusp, then C φ is not compact.

MSC:
47B38Operators on function spaces (general)
47B07Operators defined by compactness properties
30D55H (sup p)-classes (MSC2000)
46J15Banach algebras of differentiable or analytic functions, H p -spaces