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 e862fd" title="Click to view the MathML source">t>0 and f∈X, where a9134cf0350e164af3f95adce" title="Click to view the MathML source">Rtf(z)=f(eitz). We study the space of functions in X such that a8bb6">, r→1− where 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) e8a366cabfa20757bdd49ae6b3e7" title="Click to view the MathML source">‖Rtf−f‖X=O(ω(t)), (b) a94a141" title="Click to view the MathML source">‖Prf−f‖X=O(ω(1−r)), (c) ‖Δnf‖X=O(ω(2−n)), or (d) ‖f−snf‖X=O(ω(n−1)), where Prf(z)=f(rz), and e7f9b4b1464072a3a84b239ed393c" title="Click to view the MathML source">Δnf=s2nf−s2n−1f. Our results extend those known for Hardy or Bergman spaces and power weights ω(t)=tα.