论文标题
Bloom环境中的二元产品BMO
Dyadic product BMO in the Bloom setting
论文作者
论文摘要
。 Blasco和S. Pott表明，单参数HAAR乘数的所有双辅助器（带有相同符号）的运营商规范的至高无上占据了符号本身的双型二元二元产品BMO规范。在目前的工作中，我们将此结果扩展到BLOOM设置，并将其扩展到任何指数$ 1 <p <\ infty $。主要工具是在二元产品BMO中的副杂种和两次重量约翰 - 尼伦贝格的不平等方面的新特征。我们还将结果扩展到一般多参数设置中的Little BMO和乘积BMO之间的索引空间的整个尺度，在每种情况下都有适当的迭代换向器。
Ó. Blasco and S. Pott showed that the supremum of operator norms over $L^2$ of all bicommutators (with the same symbol) of one-parameter Haar multipliers dominates the biparameter dyadic product BMO norm of the symbol itself. In the present work we extend this result to the Bloom setting, and to any exponent $1<p<\infty$. The main tool is a new characterization in terms of paraproducts and two-weight John--Nirenberg inequalities for dyadic product BMO in the Bloom setting. We also extend our results to the whole scale of indexed spaces between little bmo and product BMO in the general multiparameter setting, with the appropriate iterated commutator in each case.
