刊名:Journal of Mathematical Analysis and Applications
出版年:2017
出版时间:1 January 2017
年:2017
卷:445
期:1
页码:612-630
全文大小:387 K
文摘
In this paper we deal with Banach spaces of analytic functions X defined on the unit disk satisfying that Rtf∈X for any t>0 and f∈X, where af3f95adce" title="Click to view the MathML source">Rtf(z)=f(eitz). We study the space of functions in X such that , 8a572f697" title="Click to view the MathML source">r→1− where 9ccaa1c22b69a6d7af9a00baf09b9e"> and ω is a continuous and non-decreasing weight satisfying certain mild assumptions. The space under consideration is shown to coincide with the subspace of functions in X satisfying any of the following conditions: (a) 8a366cabfa20757bdd49ae6b3e7" title="Click to view the MathML source">‖Rtf−f‖X=O(ω(t)), (b) ‖Prf−f‖X=O(ω(1−r)), (c) 9cd" title="Click to view the MathML source">‖Δnf‖X=O(ω(2−n)), or (d) 9cdc78759394ed6a567c" title="Click to view the MathML source">‖f−snf‖X=O(ω(n−1)), where 9c1accea6fd7969f55a0b1095afb8" title="Click to view the MathML source">Prf(z)=f(rz), and 8ace7f9b4b1464072a3a84b239ed393c" title="Click to view the MathML source">Δnf=s2nf−s2n−1f. Our results extend those known for Hardy or Bergman spaces and power weights 809361e9a188ad623" title="Click to view the MathML source">ω(t)=tα.