| Title:
|
Two weight norm inequalities for fractional one-sided maximal and integral operators (English) |
| Author:
|
De Rosa, Liliana |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
35-46 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we give a generalization of Fefferman-Stein inequality for the fractional one-sided maximal operator: $$ \int_{-\infty}^{+\infty} M_{\alpha}^+(f)(x)^p w(x)\,dx \leq A_p \int_{-\infty}^{+\infty} |f(x)|^p M_{\alpha p}^-(w)(x)\,dx, $$ where $0 < \alpha < 1$ and $1 < p < 1/\alpha $. We also obtain a substitute of dual theorem and weighted norm inequalities for the one-sided fractional integral $I_{\alpha}^+$. (English) |
| Keyword:
|
one-sided fractional operators |
| Keyword:
|
weighted inequalities |
| MSC:
|
26A33 |
| MSC:
|
26D10 |
| MSC:
|
42B25 |
| idZBL:
|
Zbl 1150.26310 |
| idMR:
|
MR2223965 |
| . |
| Date available:
|
2009-05-05T16:55:24Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119572 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Pérez C.: Banach function spaces and the two-weight problem for maximal functions.Proceedings of the Conference on Function Spaces, Differential Operators and Nonlinear Analysis, Paseky nad Jizerou, (1995), pp.141-158. MR 1480935 |
| Reference:
|
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| Reference:
|
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| . |
