Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 0774.30008
Jung, Il Bong; Kim, Yong Chan; Srivastava, H.M.
The Hardy space of analytic functions associated with certain one-parameter families of integral operators. (English)
[J] J. Math. Anal. Appl. 176, No.1, 138-147 (1993). ISSN 0022-247X

The authors consider classes of analytic functions $f(z)$ $(z\in U=\{\vert z\vert<1\})$ with $\Re\ f'(z)>0$ $(z\in U)$. They show (Theorem 1 and (2.16)) that the image of $f$ under a variety of integral transforms is continuous on the closed disk, and in particular belongs to all Hardy spaces $H\sb p$. (Note that $f$ itself need not even be bounded!). One such transform is $$F(z)=c\int\sb 0\sp z(\log(z/t)\sp{\alpha-1}f(t)\,dt$$ for a specific $c$ and any $\alpha>1)$. Such transforms make sense for a wider range of $\alpha$ and the authors ask if their conclusions are valid for such $\alpha$.
[D.Drasin (Lafayette)]

MSC 2000:: *30D55 H (sup p)-classes
30C45 Special classes of univalent and multivalent functions
46E20 Hilbert spaces of functions defined by smoothness properties
47B38 Operators on function spaces

Keywords: integral transforms

Cited in: Zbl 1225.30014 Zbl 1211.30024 Zbl 1200.30017 Zbl 1221.30036 Zbl 1130.30012 Zbl 1069.30043 Zbl 1056.30022 Zbl 1004.30009 Zbl 0923.30010

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]