منابع مشابه
On 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 کاملMean values of multiplicative functions
Let f(n) be a totally multiplicative function such that |f(n)| ≤ 1 for all n, and let F (s) = ∑∞ n=1 f(n)n−s be the associated Dirichlet series. A variant of Halász’s method is developed, by means of which estimates for ∑N n=1 f(n)/n are obtained in terms of the size of |F (s)| for s near 1 with 1. The result obtained has a number of consequences, particularly concerning the zeros of the p...
متن کاملA Generalized Mean Value Inequality for Subharmonic Functions and Applications
If u ≥ 0 is subharmonic on a domain Ω in Rn and p > 0, then it is well-known that there is a constant C(n, p) ≥ 1 such that u(x)p ≤C(n, p)M V (up,B(x,r)) for each ball B(x,r) ⊂ Ω. We recently showed that a similar result holds more generally for functions of the form ψ◦ u where ψ : R+ → R+ may be any surjective, concave function whose inverse ψ−1 satisfies the ∆2-condition. Now we point out tha...
متن کاملLimiting Values of Subharmonic Functions1
In 1934, Priwaloff published a generalization of Littlewood's result, which turned out to be incorrect. When the domain under consideration is the unit circle, then Priwaloff's generalization consisted in allowing "non-tangential" approaches to the boundary of the disc. In 1942, during the course of his lectures on Subharmonic functions at Brown University, the late Professor J. D. Tamarkin dis...
متن کاملDecay of Mean-values of Multiplicative Functions
p 1−f(p) p diverges then the limit in (1.1) exists, and equals 0 = Θ(f,∞). Wirsing’s result settled an old conjecture of P. Erdős and Wintner that every multiplicative function f with −1 ≤ f(n) ≤ 1 had a mean-value. The situation for complex valued multiplicative functions is more delicate. For example, the function f(n) = n (0 6= α ∈ R) does not have a mean-value because 1 x ∑ n≤x n iα ∼ x 1+i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Arkiv för Matematik
سال: 1972
ISSN: 0004-2080
DOI: 10.1007/bf02384815