Recently, a frequency-domain operator called FR-operator (where PR stands for frequency response) was defined and shown to represent the transfer characteristics of a stable sampled-data system. Using this novel frequency-domain notion and introducing its extended notion called hybrid PR-operator, we define an H-2-norm for sampled-data systems in this paper. Then, sampled-data H-2 control problems are formulated and solved, whereby the usefulness of these frequency-domain notions is demonstrated both in the analysis and synthesis aspects of sampled-data systems, For the case of sampled-data systems with hybrid (i.e., both continuous-time and discrete-time) input and output signals, the H-2-norm defined by a hybrid FR-operator turns out to be slightly different from that defined in previous studies. The source of the discrepancy is also identified.