Abstract: One of the essence of  bounded operators  is that the  image set must be bounded when the original  image set is bounded, we propose  the inverse problem of operator boundedness: how to determine the boundedness of   the original image set of an operator T  when its image set is bounded. We first introduce the concept of operator reverse boundedness, and then use weight  function method and real analysis techniques to discuss  the equivalent parametric conditions for  reverse boundedness of integral operators, and give  a construction theorem for reverse boundedness of  integral operators. Finally, some special cases are given.

Key words: non-homogeneous kernel, integral operator, reverse bounded operator, inverse Hilbert-type integral inequality, construction theorem