Functions of generalized bounded variation and its multiple fourier coefficients

摘要

Here, generalizing the class (Λ1, Λ2)*BV (p)([0, 2π]2) to the class (Λ1,Λ2)*BV (p,q)([0,2π]2) of functions of p, q-(Λ1,Λ2)*-bounded variation, it is observed that the class is a Banach space with respect to the pointwise operations and the generalized variation norm. Moreover, we estimate the order of magnitude of multiple Fourier coefficients of a function of this class.