Imbedding of Bergman spaces
For \(0<p<\infty\), \(\alpha\geq 1\) the author obtains necessary and sufficient conditions for a measure \(\mu\) in order that the Bergman space \(A^ p\) could be imbedded into the Lorentz space \(L^{\alpha p,p}(\mu)\). As a corollary, a Bergman space analogue of the Fejér-Riesz theorem is obtained. Methods used in the paper are similar to those used by \textit{E. Amar} and \textit{A. Bonami} [Bull. Soc. Math. France 107, 23-48 (1979; Zbl 0409.46035)], \textit{W. W. Hastings} [Proc. Am. Math. Soc. 52, 237-241 (1975; Zbl 0296.31009)], \textit{J. A. Cima} and \textit{W. R. Wogen} [J. Oper. Theory 7, 157-163 (1982; Zbl 0499.42011)] and \textit{D. Luecking} [Proc. Am. Math. Soc. 87, 656-660 (1983; Zbl 0521.32005)].
scientific article; zbMATH DE number 4055998
scientific article