Upper bounds for discrete moments of the derivatives of the riemann zeta-function on the critical line*

Assuming the Riemann hypothesis, we establish upper bounds for discrete moments of the Riemann zeta-function and its derivatives on the critical line. Moreover, we express continuous moments of the Riemann zeta-function and its derivatives in terms of these discrete moments. This allows us to give conditional upper bounds for $ {\int_0^T {\left| {{\zeta^{(l)}}\left( {{{1} \left/ {2} \right.} + {\text{i}}t} \right)} \right|}^{2k}}{\text{d}}t $ , where l and k are nonnegative integers.