Abstract:
Necessary and sufficient conditions governing one and two weight inequalities for
one-sided strong fractional maximal operators, one-sided and Riesz potentials with
product kernels are established on the cone of non-increasing functions. From the two–
weight results it follows criteria for the trace inequality Lp (Rn ) → Lq (v, Rn ) bound-
+
+
dec
edness
for these operators, where v, in general, is not product of one-dimensional
weights. Various type of two-weight necessary and sufficient conditions for the dis-
crete Riemann–Liouville transform with product kernels are also established. The
most of the derived two-weight results (continuous and discrete) are new even for
potentials with single kernels
