## Boundedness of some integral operators.(English)Zbl 0798.42010

The authors consider the integral operator given by $$Tf(x) = \int^ \infty_ 0 k(x,t) f(t)dt$$, where $$k:{\mathcal M} \times \mathbb{R}^ + \to \mathbb{R}^ +$$ and $$({\mathcal M},\mu)$$ is some measure space. They determine the mapping properties of $$T$$ mapping functions in $$L^ p_{dec}$$, $$0<p \leq 1$$, into functions in $$L^ q_ w$$, $$q \geq p$$; here $$L^ p_{dec}$$ is the class of nonincreasing functions in $$L^ p$$, and $$L^ q(w)$$ is a weighted $$L^ q$$ space. They also prove related weak-type inequalities and apply their results to generalized Hardy operators.