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- W1587598985 abstract "The mixed norm space $H(p,q,a)$ is the collection of functions $f$ analytic in the unit disk with finite norm $$||f||_{p,q,alpha}=left[int_{0}^{1}(1-r)^{alpha q-1}left(int_{0}^{2pi}|fleft(re^{itheta}right)|^{p} dthetaright)^{q/p}drright]^{1/q}.$$ Sufficient conditions on a family of measures ${mu_{r}:0< r <1}$ on $U$ and a measure $nu$ on $[0,1]$ are given to obtain an inequality $$||f||_{p,q,alpha}^{q}leq Cint{left(int{|f|^{p}dmu_{r}}right)^{q/p},dnu(r)},quad fin H(p,q,alpha)$$ with $C$ independent of $f$. Similar results are obtained for spaces of ``slow mean growth'' $(q=infty)$ and the Hardy spaces ($q=infty$, $alpha=0$). In the case of the Bergman spaces $(p=q)$ these conditions are an improvement over those obtained in [5] and [6]." @default.
- W1587598985 created "2016-06-24" @default.
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- W1587598985 date "1988-03-01" @default.
- W1587598985 modified "2023-10-16" @default.
- W1587598985 title "Dominating measures for spaces of analytic functions" @default.
- W1587598985 doi "https://doi.org/10.1215/ijm/1255989226" @default.
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