THE RESEARCH PROGRESS OF BNU GROUP ON RELATIVE WIDTHS
In this paper, we consider the relative n-widths of two kinds of periodic convolution classes, (K) over tilde (p)(K) and (B) over tilde (p)(G), whose convolution kernels K and G are NCVD-kernel and B-kernel. The asymptotic estimations of K(n)((K) over tilde (p)(K), (K) over tilde (p)(K))(q) and (K) over tilde (n) ((B) over tilde (p)(C), (B) over tilde (p) (C))(q) are obtained for p = 1 and infinity, 1 <= q <= infinity. We also defined a new concept of the average relative widths and obtained the exact results of the average relative widths of the classes of some smooth functions in L(2)(R(d)).
relative n-width periodic convolution class ncvd-kernel, b-kernel relative average width