TY - CHAP
T1 - Embedding (Forumula presented)
AU - Rubshtein, Ben Zion A.
AU - Grabarnik, Genady Ya
AU - Muratov, Mustafa A.
AU - Pashkova, Yulia S.
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - In this chapter, we prove the embedding theorem for classes of symmetric spaces having the same fundamental functions. The embedding theorem asserts that for every symmetric space X with a given fundamental function V = φX, there are continuous embeddings (Formula Presented). This means that the minimal part (Formula Presented) of the Lorentz space (Formula Presented) is the smallest symmetric space whose (concave) fundamental function Ṽ is equivalent to V, while the Marcinkiewicz space MV* is the largest symmetric space X with φX = φMV*= V. The renorming theorem and other consequences of the embedding theorem are considered.
AB - In this chapter, we prove the embedding theorem for classes of symmetric spaces having the same fundamental functions. The embedding theorem asserts that for every symmetric space X with a given fundamental function V = φX, there are continuous embeddings (Formula Presented). This means that the minimal part (Formula Presented) of the Lorentz space (Formula Presented) is the smallest symmetric space whose (concave) fundamental function Ṽ is equivalent to V, while the Marcinkiewicz space MV* is the largest symmetric space X with φX = φMV*= V. The renorming theorem and other consequences of the embedding theorem are considered.
UR - http://www.scopus.com/inward/record.url?scp=85006253392&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-42758-4_12
DO - 10.1007/978-3-319-42758-4_12
M3 - Chapter
AN - SCOPUS:85006253392
T3 - Developments in Mathematics
SP - 151
EP - 167
BT - Developments in Mathematics
PB - Springer New York LLC
ER -