Pointwise multipliers of Orlicz spaces

Abstract

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 esti-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.

Multiplication operators on non-commutative spaces

“…We extend this result in the setting of Orlicz spaces by showing that it holds true without the requirement that b ϕ = b ϕ1 = b ϕ2 . We use the fact that the corresponding result holds true in the commutative setting (see [25]) to establish the first part of this result.…”

Pointwise multipliers of Calderón‐Lozanovskiǐ spaces

“…General properties and several calculated concrete examples can be found in [5], [28] [38] (see also [2], [9], [11], [12], [26], [27], [31], [39] and [42]). Let us collect some of these properties and examples:…”

“…The first results on the embedding M(L ϕ 1 , L ϕ ) ֒→ L ϕ 2 , that is, for Orlicz spaces generated by Orlicz functions on non-atomic measure space, were given by Zabreȋko-Rutickiȋ [43] and Maligranda-Persson [28]. Using a recent result of Maligranda and Nakai [27] for Orlicz spaces on general σfinite measure spaces and for arbitrary Young functions we were able to adopt this proof to the situation of Calderón-Lozanovskiȋ spaces E ϕ (Theorem 5). Theorem 6 is interesting here since under certain monotonicity assumption it was possible to get also a necessary condition on Young functions for the embedding M (E ϕ 1 , E ϕ ) ֒→ E ϕ 2 .…”

Pointwise mutipliers of Orlicz function spaces and factorization

“…One of them is the following result from Maligranda-Nakaii paper [8], which states that if for two given Young functions ϕ, ϕ 1 there is a third one ϕ 2 satisfying…”