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)
Some new classes of Hardy spaces. (English) Zbl 0677.30030

The authors develop a Hardy space theory for certain function spaces, among them the spaces

B p ={fL loc 1 ():f=sup T1 [(2T) -1 -T T |f(t)| p dt] 1/p <},

1<p< (formerly considered by A. Beurling [Ann. Inst. Fourier 14, No.2, 1-32 (1964; Zbl 0133.075)]), and the harmonic extension of their elements to the upper half-plane. Their results include a Burkholder-Gundy-Silverstein maximal function characterization of spaces related to the spaces B p above. Also considered are duality relations; for example, an analogue to the Fefferman-Stein theorem [C. Fefferman and E. M. Stein, Acta Math. 129, 137-193 (1972; Zbl 0257.46078)] on the duality between the classical Hardy space H 1 and BMO is proved.

Reviewer: R.Mortini

30H05Bounded analytic functions
30D55H (sup p)-classes (MSC2000)
46J15Banach algebras of differentiable or analytic functions, H p -spaces