We propose a phenomenological study of the Balitsky-Fadin-Kuraev-Lipatov
(BFKL) approach applied to the data on the proton structure function F_2
measured at HERA in the small-x_{Bjorken} region. In a first part we use a
simplified ``effective kernel'' approximation leading to few-parameter fits of
F_2. It allows for a comparison between leading-logs (LO) and next-to-leading
logs (NLO) BFKL approaches in the saddle-point approximation, using known
resummed NLO-BFKL kernels. The NLO fits give a qualitatively satisfactory
account of the running coupling constant effect but quantitatively the chi
squared remains sizeably higher than the LO fit at fixed coupling. In a second
part, a comparison of theory and data through a detailed analysis in Mellin
space (x_{Bjorken} -> omega) leads to a more model independent approach to the
resummed NLO-BFKL kernels we consider and points out some necessary
improvements of the extrapolation at higher orders.Comment: 19 pages, 11 figures, minor corrections, one figure improved, LO fit
with reunning coupling constant and references added, conclusions unchange
