Abstract
We characterize the validity of the bilinear Hardy inequality for nonincreasing functions vertical bar vertical bar f**g**vertical bar vertical bar L-q(omega) <= C vertical bar vertical bar f vertical bar vertical bar Lambda(p1)(v(1))vertical bar vertical bar g vertical bar vertical bar Lambda(P2)(v(2)), in terms of the weights v(1,)v(2) ,omega, covering the complete range of exponents p(1), p(2), q is an element of (0, infinity]. The problem is solved by reducing it into the iterated Hardy-type inequalities (integral(infinity)(0) (integral(infinity)(0) (g**(t))(alpha) phi(t)dt)(beta backslash alpha) phi(x) dx)(1/beta) <= C(integral(infinity)(0)(g*(x))(gamma) omega(x)dx)(1/gamma), (integral(infinity)(0) (integral(infinity)(0)(g**(t))(alpha) phi(t)dt)(beta backslash alpha) phi(x) dx)(1/)beta <= C(integral(infinity)(0)(g*(x))(gamma) omega(x)dx)(1/gamma), Validity of these inequalities is characterized here for 0 < alpha< beta < infinity and 0 < gamma < infinity. 2010 Mathematics Subject Classification: 26D10, 47G10.