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 -