A space with mixed family-norm consists of all functions x on a product space such that the function [InlineMediaObject not available: see fulltext.] belongs to V (here, U(t) and V denote given Köthe spaces). Conditions for the measurability of y are given, and the Köthe dual of such spaces is determined. For this purpose a generalization of the Luxemburg-Gribanov theorem for ‘uniformly measurable’ functions is proved. This result is also formulated for vector functions.
Positivity – Springer Journals
Published: Jul 11, 2006
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