Generalization Of Hardy Inequality On N-dimension Spaces

This paper is devoted to improve the classic Hardy inequality in L~p(R~n).We get a series n-dimensional inequality analogues of the inequality of Hardy in R~1.The aim of this paper is to improve the Hardy inequality in the following two ways:(1)we get the version of hardy inequality in R~n in the means of average丨f丨in L~p(R~n) over balls of radius R centered at either 0 or x.Then we extend it to the outside of the ball.(2)We get another version of Hardy inequality in R~n in the means of average丨f丨in L~p(R~n) over squres of side丨x丨centered at either 0 or x.Furthermore we extend it to the outside of the square.