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Necessary and sufficient conditions governing two–weight estimates for one–sided potentials with multiple kernels and corresponding one–sided strong fractional maximal functions are established. The one–weight problem for the multiple Riemann–Liouville transform is also studied. Mathematics subject classification (2010): 26A33, 26D15, 46E30, 47B38.

Weighted criteria for one-sided potentials with product kernels on cones of decreasing functions