BMO, H^1, and Calderon-Zygmund operators for non doubling measures
| dc.creator | Tolsa, Xavier | |
| dc.date | 2000-02-18 | |
| dc.date.accessioned | 2026-07-07T04:33:57Z | |
| dc.date.available | 2026-07-07T04:33:57Z | |
| dc.description | Given a Radon measure $μ$ on $R^d$, which may be non doubling, we introduce a space of type BMO with respect to this measure. It is shown that many properties that hold when $μ$ is doubling remain valid for the space BMO introduced in this paper, without assuming $μ$ doubling. For instance, Calderon-Zygmund operators which are bounded in $L^2$ are bounded from $L^\infty$ into the new BMO space. Moreover, a John-Nirenberg inequality is satisfied, and the predual of BMO is an atomic space $H^1$. Using a sharp maximal function it is proved that operators bounded from $L^\infty$ into BMO and from $H^1$ into $L^1$ are also bounded on $L^p$, $1<p<\infty$. This result gives a new proof of the T(1) theorem for the Cauchy transform with non doubling measures. Finally, a result about commutators is obtained. | |
| dc.description | 58 pages | |
| dc.identifier | https://arxiv.org/abs/math/0002152 | |
| dc.identifier | http://arxiv.org/abs/math/0002152 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/58720 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | Functional Analysis | |
| dc.subject | 42B20; 42B30 | |
| dc.title | BMO, H^1, and Calderon-Zygmund operators for non doubling measures | |
| dc.type | text |