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)
Composition operators between area-type Nevanlinna classes. (English) Zbl 1223.47028

This is a translation from [J. Wuhan Univ., Nat. Sci. Ed. 50, No. 1, 1–5 (2004; Zbl 1114.47305)].

Summary: This paper is concerned with composition operators C ϕ on area-type Nevanlinna classes N a p . We give some sufficient and necessary conditions, by constructing the Carleson inequality on N a p , for the composition operator C ϕ :N a p N a q (1<pq) to be bounded or compact. In addition, we also characterize the inducing maps which induce invertible or Fredholm composition operators on N a p .

MSC:
47B33Composition operators
30H15Nevanlinna class and Smirnov class
References:
[1]Shapiro J. H., Composition operators and classical function theory, New York/Berlin: Springer-Verlag, 1993
[2]Cowen C. C. and MacCluer B. D., Composition operators on spaces of analytic functions, Boca Raton: CRC Press, 1995
[3]Smith W., Composition operators between Bergman and Hardy Spaces, Trans. Amer. Math. Soc., 1996, 348: 2331–2348 · Zbl 0857.47020 · doi:10.1090/S0002-9947-96-01647-9
[4]Choa J. S. and Kim H. O., Composition operators between Nevanlinna type spaces, J. Math. Anal. Appl., 2001, 257: 378–402 · Zbl 0997.47022 · doi:10.1006/jmaa.2000.7356
[5]Xiao J., Compact composition operators on the area-Nevanlinna class, Exposition. Math., 1999, 17: 255–264
[6]Hastings W. A., Carleson measure theorem for Bergman spaces, Proc. Amer. Math. Soc., 1975, 52: 237–241 · doi:10.1090/S0002-9939-1975-0374886-9
[7]Zhu K. H., Operator theory in function spaces, New York: Marcel Dekker, 1990
[8]Luo L. and Shi J. H., Composition operators between the weighted Bergman spaces on bounded symmetric domains of C m , Chinese Ann. Math. Ser. A, 2000, 21A(1): 45–52