Boundedness of a class of Hardy-type integral operators on rearrangement-invariant spaces is equivalent to checking only non-increasing functions, with only a constant-factor loss, on the entire positive half-line.
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Reduction principle for a certain class of kernel-type operators
Boundedness of a class of Hardy-type integral operators on rearrangement-invariant spaces is equivalent to checking only non-increasing functions, with only a constant-factor loss, on the entire positive half-line.