Multiplication operators on vector measure Orlicz spaces |
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Authors: | I. Ferrando |
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Affiliation: | a Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera, s/n, 46071 Valencia, Spain b Centro de Investigacón en Matemáticas, A. P. 402, Guanajuato, Gto., C. P. 36 000, México |
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Abstract: | Let m be a countably additive vector measure with values in a real Banach space X, and let L1(m) and Lw(m) be the spaces of functions which are, correspondingly, integrable and weakly integrable with respect to m. Given a Young's function Φ, we consider the vector measure Orlicz spaces LΦ(m) and LΦw(m) and establish that the Banach space of multiplication operators going from W = LΦ(m) into Y = L1 (m) is M = LΨw (m) with an equivalent norm; here Ψ is the conjugated Young's function for Φ. We also prove that when W = LΦw(m), Y = L1(m) we have M = LΨw (m), and when W = LΦw(m), Y = L1(m) we have M = LΨ (m). |
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Keywords: | 28B05 46E30 46G10 |
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