Qualitative Investigation of Functions in Generalized Liouville–Sobolev Function Spaces $L_p^l(E_n)$ at Infinity

The asymptotic properties, as $r=|x|$ tends to infinity, of functions from $L_p^l(E_n)$ with fractional indices $l=(l_1,\dots , l_n)$ are described with the use of spherical means. Conditions under which spherical means oscillate on $[1,\infty )$ and converge at infinity are obtained.