BMO functions and Carleson measures with values in uniformly convex spaces
| dc.creator | Ouyang, Caiheng | |
| dc.creator | Xu, Quanhua | |
| dc.date | 2007-05-14 | |
| dc.date | 2008-06-05 | |
| dc.date.accessioned | 2026-07-07T09:42:28Z | |
| dc.date.available | 2026-07-07T09:42:28Z | |
| dc.description | This paper studies the relationship between vector-valued BMO functions and the Carleson measures defined by their gradients. Let $dA$ and $dm$ denote Lebesgue measures on the unit disc $D$ and the unit circle $\mathbb T$, respectively. For $1< q<\infty$ and a Banach space $B$ we prove that there exists a positive constant $c$ such that $$\sup_{z_0\in D}\int_{D}(1-|z|)^{q-1}\|\nabla f(z)\|^q P_{z_0}(z) dA(z) \le c^q\sup_{z_0\in D}\int_{\T}\|f(z)-f(z_0)\|^qP_{z_0}(z) dm(z)$$ holds for all trigonometric polynomials $f$ with coefficients in $B$ iff $B$ admits an equivalent norm which is $q$-uniformly convex, where $$P_{z_0}(z)=\frac{1-|z_0|^2}{|1-\bar{z_0}z|^2} .$$ The validity of the converse inequality is equivalent to the existence of an equivalent $q$-uniformly smooth norm. | |
| dc.description | To appear in Canadian J. Math | |
| dc.identifier | https://arxiv.org/abs/0705.1948 | |
| dc.identifier | http://arxiv.org/abs/0705.1948 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/162194 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46E40, 42B25, 46B20 | |
| dc.title | BMO functions and Carleson measures with values in uniformly convex spaces | |
| dc.type | text |