L~p空间多元周期函数的非整数次积分

R~n空间可积函数f(x)=f(x_1,…,x_n)的非整数次积分,首先由Riesz引进,即所谓Riesz位势:

FRACTIONAL INTEGRATION OF PERIODIC FUNCTIONS OF SEVERAL VARIABLES IN L~p SPACE

In this paper has been considered L~p-eonfinuity of the fractional integration of periodic functions of several variables in the L~p space. Some results obtained are more extensive than the ordinary Riesz potentials. For example, we have established directly the equivalence of the functional space C_j~p (E~n) and the Sobolev space L_j~p (E~n).