Norm Estimates of an Integral Operator in Topological Measure Spaces

Alternative criteria for the boundedness and compactness of a Hardy-type integral operator acting in weighted Lebesgue spaces are obtained. The criteria are formulated in terms of sequences depending on the weight functions and the measures of the spaces. Conditions are found under which the ideals of compact operators coincide with the ideals generated by the sequences of s-numbers of the operator under consideration. Moreover, estimates of the operator norms in these ideals are obtained via integral expressions depending on the original weight functions.