Approximation in modified Zorko spaces

The set of smooth functions is not dense in Morrey spaces. To address the density issue in Morrey spaces, Zorko spaces are defined by utilizing the difference of a function of first order. In this paper, we propose a subspace of Morrey spaces which is defined using the difference of a function of second order. Approximation properties in the new subspace are investigated and the relation with Zorko spaces is studied via properties of smoothness spaces.