منابع مشابه
Jensen measures without regularity
In this note we construct Swiss cheeses X such that R(X) is non-regular but such that R(X) has no non-trivial Jensen measures. We also construct a non-regular uniform algebra with compact, metrizable character space such that every point of the character space is a peak point. In [Co] Cole gave a counterexample to the peak point conjecture by constructing a non-trivial uniform algebra A with co...
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We derive a new criterion for a real-valued function u to be in the Sobolev space W 1,2(Rn). This criterion consists of comparing the value of a functional R f(u) with the values of the same functional applied to convolutions of u with a Dirac sequence. The difference of these values converges to zero as the convolutions approach u, and we prove that the rate of convergence to zero is connected...
متن کاملReduced functions and Jensen measures
Let φ be a locally upper bounded Borel measurable function on a Greenian open set Ω in Rd and, for every x ∈ Ω, let vφ(x) denote the infimum of the integrals of φ with respect to Jensen measures for x on Ω. Twenty years ago, B.J. Cole and T.J. Ransford proved that vφ is the supremum of all subharmonic minorants of φ on X and that the sets {vφ < t}, t ∈ R, are analytic. In this paper, a differen...
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We give a condition on a closed set K of real n mma trices which ensures that any W p gradient Young measure sup ported on K must be trivial the condition given is also necessary when K is bounded Introduction Assume is a smooth bounded domain in R and p is a given number Let W p R be the usual Sobolev space of maps u from to R the Jacobi or gradient matrix ru of u is L integrable and thus de n...
متن کاملNearly hyperharmonic functions and Jensen measures
Let (X,H) be a P-harmonic space and assume for simplicity that constants are harmonic. Given a numerical function φ on X which is locally lower bounded, let Jφ(x) := sup{ ∫ ∗ φdμ(x) : μ ∈ Jx(X)}, x ∈ X, where Jx(X) denotes the set of all Jensen measures μ for x, that is, μ is a compactly supported measure on X satisfying ∫ u dμ ≤ u(x) for every hyperharmonic function on X. The main purpose of t...
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ژورنال
عنوان ژورنال: Studia Mathematica
سال: 2001
ISSN: 0039-3223,1730-6337
DOI: 10.4064/sm148-1-6