  The longitudinal double spin asymmetries $A_1^p$ and the spin dependent
structure function of the proton $g_1^p$ were extracted from COMPASS data in
the region of low Bjorken scaling variable $x$ and low photon virtuality $Q^2$.
The data were taken in 2007 and 2011 from scattering of polarised muons off
polarised protons, resulting in a sample that is 150 times larger than the one
from the previous experiment SMC that pioneered studies in this kinematic
region.
  For the first time, $A_1^p$ and $g_1^p$ were evaluated in this region in
two-dimensional bins of kinematic variables: $(x,Q^2)$, $(\nu ,Q^2)$, $(x,\nu)$
and $(Q^2,x)$. The following kinematic region was investigated: $4\times
10^{-5}<x<4\times 10^{-2}$, $0.001$~(GeV/$c$)$^2<Q^2<1$~(GeV/$c$)$^2$ and
$14$~GeV$<\nu <194$~GeV. The obtained results were confronted with theoretical
models.
