naa a22 4500 510760783 CHVBK 20180411083138.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s13163-011-0090-7 doi (NATIONALLICENCE)springer-10.1007/s13163-011-0090-7 Pisier Gilles Texas A&M University, 77843, College Station, TX, USA aut Real interpolation and transposition of certain function spaces [Elektronische Daten] [Gilles Pisier] Our starting point is a lemma due to Varopoulos. We give a different proof of a generalized form this lemma, that yields an equivalent description of the K-functional for the interpolation couple (X 0,X 1) where $X_{0}=L_{p_{0},\infty}(\mu_{1}; L_{q}(\mu_{2}))$ and $X_{1}=L_{p_{1},\infty}(\mu_{2}; L_{q}(\mu_{1}))$ where 0<q<p 0,p 1≤∞ and (Ω1,μ 1),(Ω2,μ 2) are arbitrary measure spaces. When q=1, this implies that the space (X 0,X 1) θ,∞ (0<θ<1) can be identified with a certain space of operators. We also give an extension of the Varopoulos Lemma to pairs (or finite families) of conditional expectations that seems of independent interest. The present paper is motivated by non-commutative applications that we choose to publish separately. Revista Matematicá Complutense, 2011 Real interpolation nationallicence K -functional nationallicence Transposition nationallicence Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 89-97 1139-1138 26:1<89 2013 26 13163 https://doi.org/10.1007/s13163-011-0090-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s13163-011-0090-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Pisier Gilles Texas A&M University, 77843, College Station, TX, USA aut NATIONALLICENCE 773 0- Revista Matemática Complutense Springer Milan 26/1(2013-01-01), 89-97 1139-1138 26:1<89 2013 26 13163 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer