论文标题
umd空间中对称奇异积分的操作员值t（1）定理
An operator-valued T(1) theorem for symmetric singular integrals in UMD spaces
论文作者
论文摘要
已知通过标量值结果建议的天然BMO（有界平均振荡）条件不足以对操作员值寄生虫的界限。因此，仅在BMO $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ t（1）的版本下才能获得运算符值的单数积分的界限。最近，Hong，Liu和Mei（J。Funct。Anal。2020）观察到，具有对称性假设的奇异积分显着改善，因此经典的$ t（1）$标准仍然保证其$ l^2 $ l^2 $ bundedness on Hilbert Space -space -valued功能。在这里，这些结果将扩展到具有相同天然BMO条件的一般UMD（无条件的Martingale差异），用于对称的副标准，此外仅需要在一般单数积分的情况下，通常需要通过$ r $ bund的统一范围来代替统一范围。特别是，在这些假设下，我们在所有$ 1 <p <\ infty $上获得了非交换性$ l^p $空间的有界性结果，而无需像Hong等人的结果那样通过相关的非交互性耐性空间替换域或目标。对于$ p \ neq 2 $。
The natural BMO (bounded mean oscillation) conditions suggested by scalar-valued results are known to be insufficient for the boundedness of operator-valued paraproducts. Accordingly, the boundedness of operator-valued singular integrals has only been available under versions of the classical ``$T(1)\in BMO$'' assumptions that are not easily checkable. Recently, Hong, Liu and Mei (J. Funct. Anal. 2020) observed that the situation improves remarkably for singular integrals with a symmetry assumption, so that a classical $T(1)$ criterion still guarantees their $L^2$-boundedness on Hilbert space -valued functions. Here, these results are extended to general UMD (unconditional martingale differences) spaces with the same natural BMO condition for symmetrised paraproducts, and requiring in addition only the usual replacement of uniform bounds by $R$-bounds in the case of general singular integrals. In particular, under these assumptions, we obtain boundedness results on non-commutative $L^p$ spaces for all $1<p<\infty$, without the need to replace the domain or the target by a related non-commutative Hardy space as in the results of Hong et al. for $p\neq 2$.
