Proper Inclusions of Function Spaces and Ryll-Wojtaszczyk Polynomials on the Unit Ball of C”

In this paper, the spaces Y_p are introduced on the unit ball of Cⁿ . The containment relations between Q_p (including BMOA and Bloch) and Y_p, B^q spaces are studied, respectively. We prove that all the inclusions: Q_p ⊂ Y_p for n − 1 n < p < n n − 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187681/bff96af3-57ee-4f14-ad65-a53036966c4e/content/inequ46_1.tif"/> , Q_p1 ⊂ Q_p for n − 1 n < p 1 < p ≤ 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187681/bff96af3-57ee-4f14-ad65-a53036966c4e/content/inequ46_2.tif"/> and ∪ n − 1 n < p < 1 Q p ⊂ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187681/bff96af3-57ee-4f14-ad65-a53036966c4e/content/inequ46_3.tif"/> for any 0 < q < 2 and ∪_{2 < q < ∞} B^q ⊂ Q_p for any 1 < p < n n − 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429187681/bff96af3-57ee-4f14-ad65-a53036966c4e/content/inequ46_4.tif"/> are proper.