| Title:
|
Weighted inequalities for integral operators with some homogeneous kernels
(English)
|
| Author:
|
Riveros, María Silvina |
| Author:
|
Urciuolo, Marta |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
423-432 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we study integral operators of the form \[ Tf(x)=\int | x-a_1y|^{-\alpha _1}\dots | x-a_my|^{-\alpha _m}f(y)\mathrm{d}y, \] $\alpha _1+\dots +\alpha _m=n$. We obtain the $L^p(w)$ boundedness for them, and a weighted $(1,1)$ inequality for weights $w$ in $A_p$ satisfying that there exists $c\ge 1$ such that $w( a_ix) \le cw( x)$ for a.e. $x\in \mathbb R^n$, $1\le i\le m$. Moreover, we prove $\Vert Tf\Vert _{{\mathrm BMO}}\le c\Vert f\Vert _\infty $ for a wide family of functions $f\in L^\infty ( \mathbb R^n)$. |
| Keyword:
|
weights |
| Keyword:
|
integral operators |
| MSC:
|
42A50 |
| MSC:
|
42B20 |
| MSC:
|
42B25 |
| idZBL:
|
Zbl 1081.42018 |
| idMR:
|
MR2137148 |
| . |
| Date available:
|
2009-09-24T11:24:05Z |
| Last updated:
|
2012-05-31 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127988 |
| . |
| 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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| . |
