| Title:
|
Commutators of sublinear operators generated by Calderón-Zygmund operator on generalized weighted Morrey spaces (English) |
| Author:
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Guliyev, Vagif Sabir |
| Author:
|
Karaman, Turhan |
| Author:
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Mustafayev, Rza Chingiz |
| Author:
|
Şerbetçi, Ayhan |
| Language:
|
English |
| Journal:
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Czechoslovak Mathematical Journal |
| ISSN:
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0011-4642 (print) |
| ISSN:
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1572-9141 (online) |
| Volume:
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64 |
| Issue:
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2 |
| Year:
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2014 |
| Pages:
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365-385 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, the boundedness of a large class of sublinear commutator operators $T_{b}$ generated by a Calderón-Zygmund type operator on a generalized weighted Morrey spaces $M_{p,\varphi }(w)$ with the weight function $w$ belonging to Muckenhoupt's class $A_{p}$ is studied. When $1<p<\infty $ and $b \in {\rm BMO}$, sufficient conditions on the pair $(\varphi _1,\varphi _2)$ which ensure the boundedness of the operator $T_{b}$ from $M_{p,\varphi _1}(w)$ to $M_{p,\varphi _2}(w)$ are found. In all cases the conditions for the boundedness of $T_{b}$ are given in terms of Zygmund-type integral inequalities on $(\varphi _1,\varphi _2)$, which do not require any assumption on monotonicity of $\varphi _1(x,r)$, $\varphi _2(x,r)$ in $r$. Then these results are applied to several particular operators such as the pseudo-differential operators, Littlewood-Paley operator, Marcinkiewicz operator and Bochner-Riesz operator. (English) |
| Keyword:
|
generalized weighted Morrey space |
| Keyword:
|
sublinear operator |
| Keyword:
|
commutator |
| Keyword:
|
BMO space |
| Keyword:
|
maximal operator |
| Keyword:
|
Calderón-Zygmund operator |
| MSC:
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42B20 |
| MSC:
|
42B25 |
| MSC:
|
42B35 |
| idZBL:
|
Zbl 06391500 |
| idMR:
|
MR3277742 |
| DOI:
|
10.1007/s10587-014-0107-8 |
| . |
| Date available:
|
2014-11-10T09:39:06Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144004 |
| . |
| Reference:
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