منابع مشابه
SUPERHARMONIC functions on foliations
We use techniques from geometric analysis to prove that any positive, leafwise superharmonic, measurable function on a Riemannian measurable foliation with transverse invariant measure, finite total volume and complete leaves is, in fact, constant on a.e. leaf.
متن کاملIntegrability of Superharmonic Functions and Subharmonic Functions
We apply the coarea formula to obtain integrability of superharmonic functions and nonintegrability of subharmonic functions. The results involve the Green function. For a certain domain, say Lipschitz domain, we estimate the Green function and restate the results in terms of the distance from the boundary.
متن کاملOn definitions of superharmonic functions
© Annales de l’institut Fourier, 1975, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier...
متن کاملOn the mean value property of superharmonic and subharmonic functions
Recall that a function u is harmonic (superharmonic, subharmonic) in an open set U ⊂ Rn (n ≥ 1) if u ∈ C2(U) and Δu = 0 (Δu ≤ 0,Δu ≥ 0) on U . Denote by H(U) the space of harmonic functions in U and SH(U) (sH(U)) the subset of C2(U) consisting of superharmonic (subharmonic) functions in U . If A ⊂ Rn is Lebesgue measurable, L1(A) denotes the space of Lebesgue integrable functions on A and |A| d...
متن کاملSuperharmonic numbers
Let τ(n) denote the number of positive divisors of a natural number n > 1 and let σ(n) denote their sum. Then n is superharmonic if σ(n) | nkτ(n) for some positive integer k. We deduce numerous properties of superharmonic numbers and show in particular that the set of all superharmonic numbers is the first nontrivial example that has been given of an infinite set that contains all perfect numbe...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1993
ISSN: 0002-9939
DOI: 10.2307/2159941