Banach function subspaces of \(L^1\) of a vector measure and related Orlicz spaces

DOI10.1016/S0019-3577(05)00004-2zbMath1087.46023MaRDI QIDQ2486113

Olvido Delgado

Publication date: 5 August 2005

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

zbMATH Keywords

Banach function spaceintegrable function

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Vector-valued set functions, measures and integrals (28B05) Vector-valued measures and integration (46G10)

Related Items (12)

Orlicz spaces associated to a quasi-Banach function space: applications to vector measures and interpolation ⋮ When and where the Orlicz and Luxemburg (quasi-) norms are equivalent? ⋮ Köthe dual of Banach lattices generated by vector measures ⋮ Optimal domains for \(L^{0}\)-valued operators via stochastic measures ⋮ On the norm with respect to vector measures of the solution of an infinite system of ordinary differential equations ⋮ Complex interpolation of Orlicz spaces with respect to a vector measure ⋮ The de la Vallée-Poussin theorem and Orlicz spaces associated to a vector measure ⋮ Vector measures: Where are their integrals? ⋮ Extending and factorizing bounded bilinear maps defined on order continuous Banach function spaces ⋮ Orlicz spaces of integrable functions with respect to vector-valued measures ⋮ Convolution structures for an Orlicz space with respect to vector measures on a compact group ⋮ Multiplication operators on vector measure Orlicz spaces

Cites Work

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• Operators into \(L^ 1\) of a vector measure and applications to Banach lattices
• The dual space of \({\mathcal L}^ 1(\mu)\) for a vector measure \(\mu\)
• When \(L^ 1\) of a vector measure is an AL-space
• Compactness properties of extended Volterra operators in \(L^p([0,1)\) for \(1\leq p \leq \infty\)]
• Integration with respect to vector measures
• On integrability and summability in vector spaces
• Banach Space Properties of L 1 of a Vector Measure
• Compactness arguments for spaces of \(p\)-integrable functions with respect to a vector measure and factorization of operators through Lebesgue-Bochner spaces

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