On certain integral means of functions of generalized bounded variation

Abstract

Abstract For certain classes of functions of Λ-bounded variation on [ - π , π ] {[-\pi,\pi]} , Waterman and D’Antonio constructed a sequence of summability kernels such that the corresponding integral means converge for any function from the class, but not for any function from a broader Λ ′ ⁢ BV {\Lambda^{\prime}\mathrm{BV}} class. In our paper, we extend this result to the case of functions of two variables.