Weighted Boundedness of the Maximal, Singular and Potential Operators in Variable Exponent Spaces
| dc.creator | Kokilashvili, V. | |
| dc.creator | Samko, S. | |
| dc.date | 2008-05-14 | |
| dc.date.accessioned | 2026-07-07T09:38:48Z | |
| dc.date.available | 2026-07-07T09:38:48Z | |
| dc.description | We present a brief survey of recent results on boundedness of some classical operators within the frameworks of weighted spaces $L^{p(\cdot)}(\varrho)$ with variable exponent $p(x)$, mainly in the Euclidean setting and dwell on a new result of the boundedness of the Hardy-Littlewood maximal operator in the space $L^{p(\cdot)}(X,\varrho)$ over a metric measure space $X$ satisfying the doubling condition. In the case where $X$ is bounded, the weight function satisfies a certain version of a general Muckenhoupt-type condition For a bounded or unbounded $X$ we also consider a class of weights of the form $\varrho(x)=[1+d(x_0,x)]^{\bt_\infty}\prod_{k=1}^m w_k(d(x,x_k))$, $x_k\in X$, where the functions $w_k(r)$ have finite upper and lower indices $m(w_k)$ and $M(w_k)$. Some of the results are new even in the case of constant $p$. | |
| dc.description | 29 pages | |
| dc.identifier | https://arxiv.org/abs/0805.2028 | |
| dc.identifier | http://arxiv.org/abs/0805.2028 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/160943 | |
| dc.subject | Functional Analysis | |
| dc.subject | 42B25; 47B38 | |
| dc.title | Weighted Boundedness of the Maximal, Singular and Potential Operators in Variable Exponent Spaces | |
| dc.type | text |