Modular convergence theorems in fractional Musielak-Orlicz spaces
Summary: Here we study modular convergence in fractional Musielak-Orlicz spaces for sequences 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 \(\varphi\) generating the space \(L^{\varphi,\alpha}\). Then the convergence theorems are obtained using a density theorem of Musielak type. For the convolution operators we also consider the line group setting.
scientific article; zbMATH DE number 549193