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Interpolation for intersections of Hardy-type spaces
Israel Journal of Mathematics ( IF 1 ) Pub Date : 2020-08-01 , DOI: 10.1007/s11856-020-2029-5
Sergei V. Kislyakov , Ilya K. Zlotnikov

Let ( X , μ ) be a space with a finite measure μ , let A and B be w *-closed subalgebras of L ∞ ( μ ), and let C and D be closed subspaces of L p ( μ ) (1 < p < ∞) that are modules over A and B , respectively. Under certain additional assumptions, the couple ( C ∩ D , C ∩ D ∩ L ∞ >( μ )) is K -closed in ( L p ( μ ), L ∞ ( μ )). This statement covers, in particular, two cases analyzed previously: that of Hardy spaces on the two-dimensional torus and that of the coinvariant subspaces of the shift operator on the circle. Furthermore, many situations when A and B are w *-Dirichlet algebras also fit in this pattern.

中文翻译:

哈代空间交集的插值

设 ( X , μ ) 是具有有限测度 μ 的空间,设 A 和 B 是 L ∞ ( μ ) 的 w *-闭子代数,并设 C 和 D 是 L p ( μ ) (1 < p < ∞) 分别是 A 和 B 上的模块。在某些额外的假设下,这对 ( C ∩ D , C ∩ D ∩ L ∞ >( μ )) 在 ( L p ( μ ), L ∞ ( μ )) 中是 K 封闭的。该陈述特别涵盖了先前分析的两种情况:二维环面上的哈代空间和圆上移位算子的共变子空间。此外,当 A 和 B 是 w *-Dirichlet 代数时,许多情况也适合这种模式。
更新日期:2020-08-01
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