Abstract
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.
Highlights
The aim of this note is to consider spaces of pointwise multipliers on Morrey spaces and weak Morrey spaces
We denote by L0 (Rn ) the space of all measurable functions from results.We denote by L0 (Rn) to R or C
The remaining part of this paper is organized as follows: In Section 2, we present our main results summarized as Tables 1–4
Summary
The aim of this note is to consider spaces of pointwise multipliers on Morrey spaces and weak Morrey spaces. The Morrey space Mq (Rn ) is the set of all Lq (Rn )-locally integrable functions f for which the norm k f kM p is finite. Morrey space wMq (Rn ) as the set of all measurable functions f ∈ L0 (Rn ) for which k f kwM p = sup λkχ(λ,∞] (| f |)kM p is finite. K gkPWM(E1 ,E2 ) ∼ k gk E3 , where the implicit constants in ∼ do not depend on g It follows from the scaling law of Morrey spaces that:. It is interesting to compare these results with the following endpoint cases: PWM( L∞ (Rn ), Mq (Rn )) = Mq (Rn ), p. The remaining part of this paper is organized as follows: In Section 2, we present our main results summarized as Tables 1–4.
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