Modular Convergence Theorems in Fractional Musielak-Orlicz Spaces

Abstract

Here we study modular convergence in fractional Musielak-Orlicz spaces for se-quences of moment type operators and convolution operators. To obtain the requested convergence properties we give some estimates for the involved operators, using a growth condition on the convex function $\phi$ generating the space $L^{\phi ,\alpha }$. Then the convergence theorems are obtained using a density theorem of Musielak type. For the convolution operators we also consider the line group setting.