A decomposition of the dual space of some Banach function spaces. (English) Zbl 1244.46011

Summary: We give a decomposition for the dual space of some Banach function spaces as the Zygmund space \(\text{EXP}_\alpha\) of the exponential integrable functions, the Marcinkiewicz space \(L^{p,\infty}\), and the Grand Lebesgue Space \(L^{p,\theta}\).


46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
Full Text: DOI


[1] C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, 1988. · Zbl 0713.68041
[2] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Pure and Applied Mathematics, vol. 146, Marcel Dekker, New York, NY, USA, 1991. · Zbl 0724.46032
[3] M. Carozza and C. Sbordone, “The distance to L\infty in some function spaces and applications,” Differential and Integral Equations, vol. 10, no. 4, pp. 599-607, 1997. · Zbl 0889.35027
[4] A. C. Zaanen, Integration, Completely Revised Edition of An Introduction to the Theory of Integration, North-Holland Publishing, Amsterdam, The Netherlands, 1967. · Zbl 0175.05002
[5] T. Iwaniec and C. Sbordone, “On the integrability of the Jacobian under minimal hypotheses,” Archive for Rational Mechanics and Analysis, vol. 119, no. 2, pp. 129-143, 1992. · Zbl 0766.46016 · doi:10.1007/BF00375119
[6] A. Fiorenza, “Duality and reflexivity in grand Lebesgue spaces,” Collectanea Mathematica, vol. 51, no. 2, pp. 131-148, 2000. · Zbl 0960.46022
[7] C. Capone and A. Fiorenza, “On small Lebesgue spaces,” Journal of Function Spaces and Applications, vol. 3, no. 1, pp. 73-89, 2005. · Zbl 1078.46017 · doi:10.1155/2005/192538
[8] M. Cwikel, “The dual of Weak Lp,” Annales de l’Institut Fourier, vol. 25, no. 2, pp. 81-126, 1975. · Zbl 0301.46025 · doi:10.5802/aif.556
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.