We present the first LOFAR observations of the radio jet in the quasar 4C+19.44 (a.k.a. PKS 1354+19) obtained with long baselines. The achieved resolution is very well matched to that of archival Jansky Very Large Array observations at higher radio frequencies as well as the archival X-ray images obtained with Chandra. We found that, for several knots along the jet, the radio flux densities measured at hundreds of MHz lie well below the values estimated by extrapolating the GHz spectra. This clearly indicates the presence of spectral curvature. Radio spectral curvature has already been observed in different source classes and/or extended radio structures, and it has been often interpreted as due to intrinsic processes, as a curved particle energy distribution, rather than absorption mechanisms (Razin-Tsytovich effect, free-free or synchrotron self absorption to name a few). Here, we discuss our results according to the scenario where particles undergo stochastic acceleration mechanisms also in quasar jet knots.