A necessary and sufficient condition for Hardy's operator in Lp(.)(0, 1). Issue 5 (29th October 2013) - Mamedov, Farman I.
Abstract The equivalent conditions are proved for the Hardy inequality xβ(.)−1∫0xf(t)dtLp(.)(0, 1)≤C∥xβ(.)f∥Lp(.)(0, 1), f≥0, to be fulfilled in the norms of a Lebesgue space with variable exponent Lp(.)(0, 1). It is assumed that the function 1β(.)−p′(.) is monotone and positive on (0, 1).