Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1211.42018
Persson, Lars-Erik; Samko, Natasha
Weighted Hardy and potential operators in the generalized Morrey spaces.
(English)
[J] J. Math. Anal. Appl. 377, No. 2, 792-806 (2011). ISSN 0022-247X

The authors study the weighted $p\rightarrow q$-boundedness of the multi-dimensional Hardy type operators in the generalized Morrey spaces $\cal L^{p,\varphi }(\Bbb R^n, w)$ defined by an almost increasing function $\varphi (r)$ and radial type weight $w(|x|)$ from the Bary-Stechkin-type class. Sufficient conditions are obtained, in terms of some integral inequalities imposed on $\varphi$ and $w$, for such a $p\rightarrow q$-boundedness. In the case of local spaces the obtained conditions are also necessary. These results are applied to derive a similar weighted $p\rightarrow q$-boundedness of the Riesz potential operator.
[Lubomira Softova (Aversa)]
MSC 2000:
*42B25 Maximal functions
47B38 Operators on function spaces
47G40

Keywords: generalized Morrey spaces; weighted Hardy operator; weighted Hardy inequalities; Riesz potential operator; Bary-Stechkin classes; Matuszewska-Orlicz indices

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences