In this article, we study the weak and extra-weak type integral inequalities for the modified integral Hardy operators. We provide suitable conditions on the weights omega, rho, phi and psi to hold the following weak type modular inequality u(-1)(integral({vertical bar If vertical bar>gamma} )u(gamma omega)rho) gamma}( )<= u omicron nu(-1)(integral(infinity)(0) nu(integral(infinity)(0) nu(C vertical bar f vertical bar phi/gamma)psi). Further, we discuss the above two inequalities for the conjugate of the modified integral Hardy operators. It will extend the existing results for the Hardy operator and its integral version.
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