VECTOR-VALUED FUNCTIONS INTEGRABLE WITH RESPECT TO BILINEAR MAPS

作     者：Blasco, O. Calabuig, J. M. 

作者机构：Univ Valencia Dept Math E-46100 Burjassot Spain Univ Politecn Valencia Dept Appl Math Valencia 46022 Spain 

出 版 物：《TAIWANESE JOURNAL OF MATHEMATICS》 (Taiwanese J. Math.)

年 卷 期：2008年第12卷第9期

页      面：2387-2403页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Proyecto [BMF2005-08350-C03-03  MTN2004-21420-E] 

主　　题：Vector-valued functions Bilinear map 

摘      要：Let (Omega,Sigma,mu) be a sigma-finite measure space, 1 Z be a bounded bilinear map. We say that an X-valued function is p-integrable with respect to B whenever sup{integral(Omega) parallel to B(f(w), y parallel to(p) d mu : parallel to y parallel to = 1} is finite. We identify the spaces of functions integrable with respect to the bilinear maps arising from Holder s and Young s inequalities. We apply the theory to give conditions on X-valued kernels for the boundedness of integral operators TB(f)(w) = integral(Omega ) B(k(w, w ), f(w ))d mu (w ) from L-p(Y) into L-p(Z), extending the results known in the operator-valued case, corresponding to B : L(X, Y) x X - Y given by B(T, x) = Tx.