# A Note on Rectangular Morrey-Campanato Spaces

### New Zealand Journal of Mathematics

Vol. 47, (2017), Pages 111-119

Carolina Espinoza-Villalva

Departamento de Matematicas,

Rosales y Luis Encinas,

Hermosillo, Sonora, 83000,

Mexico.

Abstract We define rectangular central versions of the Campanato and Morrey spaces in $\mathbb{R}^2$ and consider the commutator operator of the rectangular 2-dimensional Hardy operator and a locally integrable function b acting on these Morrey spaces. We prove continuity of this operator when b belongs to a rectangular central Campanato space.

Keywords Rectangular Morrey-Campanato spaces, commutators, Hardy operator

Classification (MSC2000) Primary 47B47; Secondary 42B35.