[en] We report on low-T (T≥0.02 K) measurements of the electrical resistivity, ρ(T,B), and the magnetic AC-susceptibility, χ_ac(T,B), on the low-carrier density, one-dimensional S=((1)/(2)) antiferromagnet Yb₄As₃ in magnetic fields B≤19 T. For 2 K≤T≤20 K we find ρ-ρ₀=AT² (ρ₀: residual resistivity), with a large coefficient A∼0.75 μΩ cm/K² followed by a minimum around 1 K and a 0.1% increase for T→0. In finite fields and below about 5 K, ρ(T,B) shows a history-dependent hysteretic behavior. The oscillatory behavior superimposed is attributed to the Shubnikov-de Haas effect arising from a low density of mobile As-p holes. For T≥0.4 K, χ_ac(T) follows the prediction of the quantum sine-Gordon model. A cusp-like anomaly is found at 0.15 K