Valuations on Orlicz spaces and \(L^\phi\)-star sets

DOI10.1016/j.aam.2013.07.004zbMath1301.46009OpenAlexW2029984718MaRDI QIDQ395240

Hassane Kone

Publication date: 29 January 2014

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2013.07.004

zbMATH Keywords

valuationsOrlicz spaces

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) Dissections and valuations (Hilbert's third problem, etc.) (52B45)

Related Items (17)

Valuations on the Space of Quasi-Concave Functions ⋮ Real-valued valuations on Sobolev spaces ⋮ Radial continuous rotation invariant valuations on star bodies ⋮ Laplace transforms and valuations ⋮ Translation invariant valuations on quasi-concave functions ⋮ Orlicz-Lorentz centroid bodies ⋮ A homogeneous decomposition theorem for valuations on convex functions ⋮ Minkowski valuations on convex functions ⋮ Existence of solutions to the Orlicz-Minkowski problem ⋮ Volume, polar volume and Euler characteristic for convex functions ⋮ A flow method for the dual Orlicz–Minkowski problem ⋮ Hessian valuations ⋮ Monotone valuations on the space of convex functions ⋮ A class of invariant valuations on \(\operatorname{Lip}(S^{n -1})\) ⋮ The support of dually epi-translation invariant valuations on convex functions ⋮ Valuations on convex functions and convex sets and Monge-Ampère operators ⋮ \(L_p\)-Minkowski valuations on \(L^q\)-spaces

Cites Work

• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• Fisher information and matrix-valued valuations
• Invariant valuations on star-shaped sets
• Theory of valuations on manifolds. II
• Orlicz centroid bodies
• The even Orlicz Minkowski problem
• Orlicz projection bodies
• Star valuations and dual mixed volumes
• Valuations and surface area measures
• Minkowski valuations on $L^{p}$-spaces
• Valuations on Sobolev spaces
• Blaschke valuations
• Valuations on Lp-Spaces
• $\mathrm{GL}(n)$ contravariant Minkowski valuations
• Even valuations on convex bodies
• $GL(n)$ equivariant Minkowski valuations
• SL(n)-covariantL_p-Minkowski valuations
• Fubini Theorems for Orlicz Spaces of Lebesgue-Bochner Measurable Functions
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