Abstract
If X is any of the separable Hardy or mixed norm spaces, then the spaces \(X^{\prime }\), \(X^a\), \((X,H^{\infty })\) and \((X,\mathcal A)\) all coincide; see Sect. 1.3.2. Using this fact, we describe the duals of the separable Hardy spaces and of mixed norm spaces.
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References
Rudin, W.: Real and Complex Analysis, 3rd edn. McGraw-Hill, New York (1987)
Piranian, G., Shields, A.L., Wells, J.H.: Bounded analytic functions and absolutely continuous measures. Proc. Am. Math. Soc. 18, 818–826 (1967)
Zygmund, A.: Trigonometric series, 2nd edn, vols. I and II. Cambridge University Press, London (1968)
Duren, P.L., Romberg, B.W., Shields, A.L.: Linear functionals on \(H^p\) spaces with \(0<p<1,\). J. Reine Angew. Math. 238, 32–60 (1969)
Benedek, A., Panzone, R.: The space \(L^p\), with mixed norm. Duke Math. J. 28, 301–324 (1961)
Caveny, J.: Bounded Hadamard products of \(H^p\) functions. Duke Math. J. 33, 389–394 (1966)
Caveny, J.: Absolute convergence factors for \(H^p\) series. Can. J. Math. 21, 187–195 (1969)
Wells, J.H.: Some results concerning multipliers of \(H^p\). J. Lond. Math. Soc. 2, 549–556 (1970)
Romberg, B.W.: The \(H_p\) spaces with \(0<p<1\), Doctoral dissertation, Univ. of Rochester (1960)
Shapiro, J.H.: On being Allen’s student. Math. Intell. 12(2), 15–17 (1990)
Taibleson, M.H.: On the theory of Lipschitz spaces of distributions on Euclidean \(n\)-space II, Translation invariant operators, duality and interpolation. J. Math. Mech. 14, 821–839 (1965)
Ahern, P., Jevtić, M.: Duality and multipliers for mixed norm spaces. Michigan Math. J. 30, 53–64 (1983)
Shapiro, J.H.: Linear functionals on non-linear convex spaces. Ph.D. Thesis, University of Michigan, Ann Arbor (1969)
Flett, T.M.: Lipschitz spaces of functions on the circle and the disk. J. Math. Anal. Appl. 39, 125–158 (1972)
Pavlović, M.: Mixed norm spaces of analytic and harmonic functions I. Publ. Inst. Math. 40(54), 117–141 (1986)
Pavlović, M.: Mixed norm spaces of analytic and harmonic functions II. Publ. Inst. Math. 41(55), 97–110 (1987)
Shields, A.L., Williams, D.L.: Bounded projections, duality and multipliers in spaces of harmonic functions. J. Reine Angew. Math. 299(300), 256–279 (1978)
Jevtić, M., Pavlović, M.: On the Hahn–Banach extension property in hardy and mixed norm spaces on the unit ball. Monatshefte fur Mathematik 111, 137–145 (1991)
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Jevtić, M., Vukotić, D., Arsenović, M. (2016). Duality and Multipliers. In: Taylor Coefficients and Coefficient Multipliers of Hardy and Bergman-Type Spaces. RSME Springer Series, vol 2. Springer, Cham. https://doi.org/10.1007/978-3-319-45644-7_10
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DOI: https://doi.org/10.1007/978-3-319-45644-7_10
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