Orlicz spaces which are Lp-spaces. (Summary).
Orlicz spaces, α-decreasing functions, and the Δ₂ condition
We prove some quantitatively sharp estimates concerning the Δ₂ and ∇₂ conditions for functions which generalize known ones. The sharp forms arise in the connection between Orlicz space theory and the theory of elliptic partial differential equations.
Orlicz-Morrey spaces and the Hardy-Littlewood maximal function
We prove basic properties of Orlicz-Morrey spaces and give a necessary and sufficient condition for boundedness of the Hardy-Littlewood maximal operator M from one Orlicz-Morrey space to another. For example, if f ∈ L(log L)(ℝⁿ), then Mf is in a (generalized) Morrey space (Example 5.1). As an application of boundedness of M, we prove the boundedness of generalized fractional integral operators, improving earlier results of the author.
Orlicz-Pettis topologies in function spaces.
Orlicz-Sobolev spaces with zero boundary values on metric spaces.
Orthogonal bases in 1∞ (X).
Orthogonal bases in a topological algebra are Schauder bases.
Orthogonal constant mappings in isosceles orthogonal spaces
Orthogonal decompositions in Hilbert -modules and stationary processes.
Orthogonal Expansion of Vector-Valued Functions and Measures
Orthogonal Forms and Probability in von Neumann Algebras.
Orthogonal harmonic analysis of fractal measures.
Orthogonal scalar products on von Neumann algebras
Orthogonal Trigonometric Schauder Bases of Optimal Degree for C(K).
Orthogonal vector measures on projection lattices in a Hilbert space
Orthogonality and additive functions on normed linear spaces
Orthogonality in normed linear spaces: a classification of the different concepts and some open problems.
Orthogonality in inner products is a binary relation that can be expressed in many ways without explicit mention to the inner product of the space. Great part of such definitions have also sense in normed linear spaces. This simple observation is at the base of many concepts of orthogonality in these more general structures. Various authors introduced such concepts over the last fifty years, although the origins of some of the most interesting results that can be obtained for these generalized concepts...
Orthogonalkompakte Teilmengen topologischer Vektorverbände.
Orthogonally additive functionals on
In this paper we give a representation theorem for the orthogonally additive functionals on the space in terms of a non-linear integral of the Henstock-Kurzweil-Stieltjes type.
Orthogonally additive mappings on Hilbert modules
We study the representation of orthogonally additive mappings acting on Hilbert C*-modules and Hilbert H*-modules. One of our main results shows that every continuous orthogonally additive mapping f from a Hilbert module W over 𝓚(𝓗) or 𝓗𝓢(𝓗) to a complex normed space is of the form f(x) = T(x) + Φ(⟨x,x⟩) for all x ∈ W, where T is a continuous additive mapping, and Φ is a continuous linear mapping.