WEIGHTED HARDY-TYPE INEQUALITIES IN ORLICZ SPACES

For a given N-function M, and inner and outer weight functions omega, e-(phi), we obtain Hardy-type inequalities: integral(b)(a) M(omega(r)vertical bar u(r)vertical bar)e(-phi(r))dr <= C (integral(b)(a) M(vertical bar u(r)vertical bar)e(-phi(r))dr + integral(b)(a) M(vertical bar u'(r)vertical bar)e(-phi(r))dx), holding for every u is an element of R, where R is a suitable dilation invariant subset of W-loc(1,1)(a, b), containing C-0(infinity) (a, b). The constant C above is independent of u. In many cases considered, the set R is proven to be maximal possible.