Abstract:
Two–weight criteria of various type for one–sided maximal functions and one–sided
potentials are established in variable exponent Lebesgue spaces. Among other re-
sults we derive the Hardy–Littlewood, Fefferman–Stein and trace inequalities in these
spaces. Weighted estimates for Hardy–type, maximal, potential and singular opera-
tors defined by means of a quasi–metric and a doubling measure are derived in Lp(x)
spaces. In some cases examples of weights guaranteeing the appropriate weighted
estimates are given.
