Carleson measures in Hardy and weighted Bergman spaces of polydiscs
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- by F. Jafari PDF
- Proc. Amer. Math. Soc. 112 (1991), 771-781 Request permission
Abstract:
The importance of theorems on Carleson measures has been well recognized [3]. In [1] Chang has given a characterization of the bounded measures on ${L^p}({T^n})$ using what one may characterize as the bounded identity operators from Hardy spaces of polydiscs in ${L^p}$ spaces. In [4] Hastings gives a similar result for (unweighted) Bergman spaces of polydiscs. In this paper we characterize the bounded identity operators from weighted Bergman spaces of polydiscs into ${L^p}$ spaces, and classify those operators which are compact on the Hardy and weighted Bergman spaces in terms of Carleson-type conditions. We give two immediate applications of these results here, and a much broader class of applications elsewhere [5].References
- Sun-Yung A. Chang, Carleson measure on the bi-disc, Ann. of Math. (2) 109 (1979), no.Β 3, 613β620. MR 534766, DOI 10.2307/1971229
- Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
- John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
- William W. Hastings, A Carleson measure theorem for Bergman spaces, Proc. Amer. Math. Soc. 52 (1975), 237β241. MR 374886, DOI 10.1090/S0002-9939-1975-0374886-9
- F. Jafari, On bounded and compact composition operators in polydiscs, Canad. J. Math. 42 (1990), no.Β 5, 869β889. MR 1081000, DOI 10.4153/CJM-1990-045-0 β, Composition operators in polydiscs, Dissertation, University of Wisconsin, Madison, 1989.
- Barbara D. MacCluer, Compact composition operators on $H^p(B_N)$, Michigan Math. J. 32 (1985), no.Β 2, 237β248. MR 783578, DOI 10.1307/mmj/1029003191
- Barbara D. MacCluer and Joel H. Shapiro, Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canad. J. Math. 38 (1986), no.Β 4, 878β906. MR 854144, DOI 10.4153/CJM-1986-043-4
- Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594
- David A. Stegenga, Multipliers of the Dirichlet space, Illinois J. Math. 24 (1980), no.Β 1, 113β139. MR 550655
Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 112 (1991), 771-781
- MSC: Primary 47B38; Secondary 32A35, 46E15, 47B07
- DOI: https://doi.org/10.1090/S0002-9939-1991-1039533-0
- MathSciNet review: 1039533