Geodesic
Qualitative Investigation of Functions in Generalized Liouville--Sobolev Function Spaces $L_p^l(E_n)$ at Infinity
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 285-293

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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. 
@article{TM_2005_248_a25,
     author = {S. V. Uspenskii and E. N. Vasil'eva},
     title = {Qualitative {Investigation} of {Functions} in {Generalized} {Liouville--Sobolev} {Function} {Spaces} $L_p^l(E_n)$ at {Infinity}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {285--293},
     publisher = {mathdoc},
     volume = {248},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2005_248_a25/}
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S. V. Uspenskii; E. N. Vasil'eva. Qualitative Investigation of Functions in Generalized Liouville--Sobolev Function Spaces $L_p^l(E_n)$ at Infinity. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Studies on function theory and differential equations, Tome 248 (2005), pp. 285-293. http://geodesic.mathdoc.fr/item/TM_2005_248_a25/