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)
Real-variable characterizations of Hardy spaces associated with Bessel operators. (English) Zbl 1227.42021
The authors prove characterizations of the atomic Hardy spaces $H^p((0,\infty),dm_\lambda)$ associated with the Bessel operator $\Delta_\lambda = -\frac{d^2}{dx^2}-\frac{2\lambda}x\frac d{dx} $, where $dm_\lambda(x)=x^{2\lambda}dx$, $p\in ((2\lambda+1)\slash(2\lambda+2),1]$ and $\lambda\in(0,\infty)$. The characterizations are given in terms of the radial maximal function, the nontangential maximal function, the grand maximal function, the Littlewood-Paley $g$-function and the Lusin area function. Arguments in the proofs are partially based on results and notions introduced by {\it Y.-S. Han, D. Müller} and {\it D.-C. Yang} in [Math. Nachr. 279, No. 13--14, 1505--1537 (2006; Zbl 1179.42016)] and [Abstr. Appl. Anal. 2008, Article ID 893409 (2008; Zbl 1193.46018)].

42B30$H^p$-spaces (Fourier analysis)
42B25Maximal functions, Littlewood-Paley theory
42B35Function spaces arising in harmonic analysis
Full Text: DOI arXiv