Abstract
We consider weighted bounds for quasilinear integral operators of the form from to on the set on non- negative and non- negative monotone functions , where , and are weight functions. Under the assumption that , we obtain necessary and sufficient conditions for the validity of these bounds on the set of non- negative functions for the values of the parameters satisfying the conditions and , , and also on the cones of non- negative non-increasing and non- negative non- decreasing functions for and . Here it is assumed only that . However, the criteria we obtain involve the norm of a linear integral operator from to with kernel .
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