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Fubini theorems for Orlicz spaces of Lebesgue-Bochner measurable functions
| Content Provider | Semantic Scholar |
|---|---|
| Author | Zander, Vernon |
| Copyright Year | 1972 |
| Abstract | Let (X, V, v) be the volume space formed as the product of the volume spaces (Xi, Vi, v) (i=1, 2). Let (p, q) be a pair of complementary (continuous) Young's functions, let Y, Z, Z1, Z2, W be Banach spaces, let w be a multilinear continuous operator on YxZlxZ2-*W. Let L(v, Y) be the Orlicz space of Lebesgue-Bochner measurable functions generated by p, and let Kq(v, Z) be the associated space of finitely additive Z-valued set functions. The principal result of this paper is as follows: Let fCL(v, Y), [2CK (b) the operator r(f, MD2) defined by the expression r(f, 1t2)(X) = f Wl(f (Xl, X2), a2(dx2)) vl-a.e. is bilinear and continuous from L(v, Y) XKq(V2, Z2) into Lj,(vl, Y1)/N, where wl(y, Z2) = w(y, Z2), where Y1 is the Banach space of bounded linear operators from Z, into W, and where N is the set of Y1valued vl-measurable functions of zero seminorm; (c) the equality f w(f, d,il, d,2)=f w0(r(f, Iu2), d,y) holds for all fCL(v, Y), ujK received by the editors March 20, 1970 and, in revised form, February 1, 1971. AMS 1970 subject classifications. Primary 28A35, 28A40, 46E30; Secondary 28A25, 28A45, 46GI0, 46E40. |
| Starting Page | 102 |
| Ending Page | 110 |
| Page Count | 9 |
| File Format | PDF HTM / HTML |
| DOI | 10.1090/S0002-9939-1972-0291791-4 |
| Alternate Webpage(s) | http://www.ams.org/journals/proc/1972-032-01/S0002-9939-1972-0291791-4/S0002-9939-1972-0291791-4.pdf |
| Alternate Webpage(s) | https://www.ams.org/journals/proc/1972-032-01/S0002-9939-1972-0291791-4/S0002-9939-1972-0291791-4.pdf |
| Alternate Webpage(s) | https://doi.org/10.1090/S0002-9939-1972-0291791-4 |
| Volume Number | 32 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
