## Extension of the best approximation operator in Orlicz spaces.(English)Zbl 1160.41308

The authors study an extension of the best approximation operator from an Orlicz space $$L^\phi$$ to $$L^{\phi'}$$.

### MSC:

 41A35 Approximation by operators (in particular, by integral operators) 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) 47B38 Linear operators on function spaces (general)

### Keywords:

Orlicz space; best approximation operator
Full Text:

### References:

 [1] D. Landers and L. Rogge, “Best approximants in L\varphi -spaces,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 51, no. 2, pp. 215-237, 1980. · Zbl 0422.60039 [2] D. Landers and L. Rogge, “Isotonic approximation in Ls,” Journal of Approximation Theory, vol. 31, no. 3, pp. 199-223, 1981. · Zbl 0467.41014 [3] F. Mazzone and H. Cuenya, “Isotonic approximations in L1,” Journal of Approximation Theory, vol. 117, no. 2, pp. 279-300, 2002. · Zbl 1012.41025 [4] S. Favier and F. Zó, “Extension of the best approximation operator in Orlicz spaces and weak-type inequalities,” Abstract and Applied Analysis, vol. 6, no. 2, pp. 101-114, 2001. · Zbl 0999.41010 [5] S. Favier and F. Zó, “A Lebesgue type differentiation theorem for best approximations by constants in Orlicz spaces,” Real Analysis Exchange, vol. 30, no. 1, pp. 29-42, 2005. · Zbl 1068.41047 [6] S. Favier and F. Zó, “Sharp conditions for maximal inequalities of the best approximation operator,” preprint. · Zbl 1399.41017 [7] F. Mazzone and H. Cuenya, “Maximal inequalities and Lebesgue’s differentiation theorem for best approximant by constant over balls,” Journal of Approximation Theory, vol. 110, no. 2, pp. 171-179, 2001. · Zbl 0979.41017 [8] H. D. Brunk and S. Johansen, “A generalized Radon-Nikodym derivative,” Pacific Journal of Mathematics, vol. 34, pp. 585-617, 1970. · Zbl 0183.48302 [9] F. Mazzone and H. Cuenya, “A characterization of best \varphi -approximants with applications to multidimensional isotonic approximation,” Constructive Approximation, vol. 21, no. 2, pp. 207-223, 2005. · Zbl 1067.41014 [10] J. Neveu, Mathematical Foundations of the Calculus of Probability, Holden-Day, San Francisco, Calif, USA, 1965. · Zbl 0137.11301
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.