TY - JOUR
T1 - On the compactness in grand spaces
AU - Rafeiro, Humberto
AU - Vargas, Andrés
N1 - Publisher Copyright:
© 2015 Walter de Gruyter GmbH.
PY - 2015/3/1
Y1 - 2015/3/1
N2 - In this paper we study compactness of subsets of grand Lebesgue spaces (also known as Iwaniec-Sbordone spaces) and grand Sobolev spaces. Namely, we prove a Kolmogorov-Riesz compactness theorem for grand Lebesgue spaces and the corresponding version of a result of Sudakov. In addition, the validity of a Rellich-Kondrachov type compact embedding is shown to hold in the context of grand Sobolev spaces.
AB - In this paper we study compactness of subsets of grand Lebesgue spaces (also known as Iwaniec-Sbordone spaces) and grand Sobolev spaces. Namely, we prove a Kolmogorov-Riesz compactness theorem for grand Lebesgue spaces and the corresponding version of a result of Sudakov. In addition, the validity of a Rellich-Kondrachov type compact embedding is shown to hold in the context of grand Sobolev spaces.
KW - Grand Lebesgue spaces
KW - Kolmogorov compactness
KW - Rellich-Kondrachov compactness
KW - grand Sobolev spaces
UR - http://www.scopus.com/inward/record.url?scp=84925807787&partnerID=8YFLogxK
U2 - 10.1515/gmj-2014-0060
DO - 10.1515/gmj-2014-0060
M3 - Article
AN - SCOPUS:84925807787
SN - 1072-947X
VL - 22
SP - 141
EP - 152
JO - Georgian Mathematical Journal
JF - Georgian Mathematical Journal
IS - 1
ER -