Archiv der Mathematik

, Volume 95, Issue 3, pp 251–256 | Cite as

Pointwise multipliers of Orlicz spaces

Article

Abstract

We show that the result on multipliers of Orlicz spaces holds in general. Namely, under the assumption that three Young functions Φ1, Φ2 and Φ, generating corresponding Orlicz spaces, satisfy the estimate \({\Phi^{-1}(u) \leq C \Phi_1^{-1}(u)\, \Phi_2^{-1}(u)}\) for all u > 0, we prove that if the pointwise product xy belongs to LΦ(μ) for all \({y \in L^{\Phi_1}(\mu)}\), then \({x \in L^{\Phi_2}(\mu)}\). The result with some restrictions either on Young functions or on the measure μ was proved by Maligranda and Persson (Indag. Math. 51 (1989), 323–338). Our result holds for any collection of three Young functions satisfying the above estimate and for an arbitrary complete σ-finite measure μ.

Mathematics Subject Classification (2000)

46E30 46B42 

Keywords

Orlicz spaces Pointwise multipliers Pointwise multiplicatión 

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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Department of MathematicsLuleå University of TechnologyLuleåSweden
  2. 2.Department of MathematicsOsaka Kyoiku UniversityKashiwara, OsakaJapan

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