Norm inequalities in Dunkl-type total Fofana-Guliyev spaces

Abstract

We introduce total Fofana-Guliyev spaces associated with the Dunkl operator on the real line called Dunkl-type total Fofana-Guliyev spaces and investigate their basic properties. We show that these spaces generalize Dunkl-Fofana spaces and are subspaces of Dunkl total Morrey spaces. As applications, we establish norm inequalities for the Dunkl-type Hardy-Littlewood maximal operator, Dunkl-type fractional integral operators and Dunkl-type fractional maximal operators in Dunkl-type total Fofana-Guliyev spaces.