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.
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