DOI: 10.1515/anly-2023-0073 ISSN: 0174-4747

Generalized Morrey spaces and multiplication operators

René Erlin Castillo, Juan Felipe González Ostos, Héctor Camilo Chaparro
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Abstract

In this paper, we study some properties of generalized Morrey spaces

ℳ p , ϕ ⁢ ( ℝ n ) {\mathcal{M}^{p,\phi}(\mathbb{R}^{n})}
. Multiplication operators
M u {M_{u}}
(which are a class of operators that generalize the notion of operator given by a diagonal matrix) defined on such spaces are also studied. In particular, we obtain results about
M u {M_{u}}
(e.g., when it is an isometry, its boundedness, etc.). It is shown that the multiplication operator is a self-adjoint operator. Finally, its compactness is also characterized.

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