| Title:
|
Boundedness of one-sided fractional integrals in the one-sided Calderón-Hardy spaces (English) |
| Author:
|
Perini, Alejandra |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2011 |
| Pages:
|
57-75 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study the mapping properties of the one-sided fractional integrals in the Calderón-Hardy spaces $\mathcal{H}_{q,\alpha}^{p,+}(\omega)$ for $0< p\leq 1$, $0< \alpha < \infty $ and $1< q< \infty $. Specifically, we show that, for suitable values of $p,q,\gamma, \alpha$ and $s$, if $\omega \in A_s^+$ (Sawyer's classes of weights) then the one-sided fractional integral $I_{\gamma }^+$ can be extended to a bounded operator from $\mathcal{H}_{q,\alpha}^{p,+}(\omega)$ to $\mathcal{H}_{q,\alpha + \gamma}^{p,+}(\omega)$. The result is a consequence of the pointwise inequality $$ N_{q, \alpha +\gamma}^+\left( I_{\gamma }^+ F;x\right) \leq C_{\alpha,\gamma } N_{q, \alpha}^+ \left( F;x\right), $$ where $N_{q, \alpha}^+ (F;x)$ denotes the Calderón maximal function. (English) |
| Keyword:
|
fractional integral |
| Keyword:
|
maximal |
| Keyword:
|
one-sided Calderón-Hardy |
| Keyword:
|
one-sided weights spaces |
| MSC:
|
42B20 |
| MSC:
|
42B35 |
| idZBL:
|
Zbl 1240.42061 |
| idMR:
|
MR2828370 |
| . |
| Date available:
|
2011-03-08T17:37:04Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141428 |
| . |
| 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:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
