Spaces of Pointwise Multipliers on Morrey Spaces and Weak Morrey Spaces

The spaces of pointwise multipliers on Morrey spaces are described in terms of Morrey spaces, their preduals, and vector-valued Morrey spaces introduced by Ho. This paper covers weak Morrey spaces as well. The result in the present paper completes the characterization of the earlier works of the first author’s papers written in 1997 and 2000, as well as Lemarié-Rieusset’s 2013 paper. As a corollary, the main result in the present paper shows that different quasi-Banach lattices can create the same vector-valued Morrey spaces. The goal of the present paper is to provide a complete picture of the pointwise multiplier spaces.

Pointwise multipliers between weighted copson and cesàro function spaces

In this paper the solution of the pointwise multiplier problem between weighted Copson function spaces Copp1,q1(u1, v1) and weighted Cesàro function spaces Cesp2,q2(u2, v2) is presented, where p1, p2, q1, q2 ∈ (0, ∞), p2 ≤ q2 and u1, u2, v1, v2 are weights on (0, ∞).

Multipliers in Holomorphic Mean Lipschitz Spaces on the Unit Ball

For1≤p≤∞ands>0,letΛspbe holomorphic mean Lipschitz spaces on the unit ball inℂn. It is shown that, ifs>n/p,the spaceΛspis a multiplicative algebra. Ifs>n/p, then the spaceΛspis not a multiplicative algebra. We give some sufficient conditions for a holomorphic function to be a pointwise multiplier ofΛn/pp.