APPROXIMATION BY M. RIESZ KERNELS IN L~p FOR p < 1

摘要

Let α > 0. We consider the linear span X_α(R~n) of scalar Riesz's kernels {1/(|x-a|~α)}_(α∈R~n) and the linear span Y_α(R~n) of vector Riesz's kernels {1/(|x-a|~(α+1))(x - a)}_(α∈R~n). We study the following problems. (1) When is the intersection X_α(R~n) ∩ L~p(R~n) dense in L~p(R~n)? (2) When is the intersection Y_α(R~n) ∩ L~p(R~n, R~n) dense in L~p(R~n, R~n) ?