THE K-T-FUNCTIONAL FOR THE INTERPOLATION COUPLE L(INFINITY)(D-MU, L(1)(DV)), L(INFINITY)(DV, L(1)(D-MU)) Academic Article uri icon

abstract

  • Let $(M,mu)$ and $(N,
    u)$ be measure spaces. In this paper, we study the $K_t$--,functional for the couple $$A_0=L^infty(dmu,; L^1(d
    u)),,~~A_1=L^infty(d
    u,; L^1(dmu)),. $$ Here, and in what follows the vector valued $L^p$--,spaces $L^p(dmu,; L^q(d
    u))$ are meant in Bochner's sense. One of our main results is the following, which can be viewed as a refinement of a lemma due to Varopoulos [V]. proclaim Theorem 0.1. Let $(A_0,A_1)$ be as above. Then for all $f$ in $A_0+A_1$ we have $${1over 2},K_t(f;,A_0,,A_1)leq sup,\bigg{ Big(mu(E)vee t^{-1}
    u(F)Big)^{-1} int_{E imes F} vert fvert,dmu,d
    u,\bigg} leq K_t(f;,A_0,,A_1),,$$ where the supremum runs over all measurable subsets $Esubset M,,~ Fsubset N$ with positive and finite measure and $u!vee!v$ denotes the maximum of the reals $u$ and $v$.

published proceedings

  • QUARTERLY JOURNAL OF MATHEMATICS

author list (cited authors)

  • HESS, A., & PISIER, G.

citation count

  • 4

complete list of authors

  • HESS, A||PISIER, G

publication date

  • September 1995