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Tail probability and singularity of Laplace-Stieltjes transform of a Pareto type random variable

Kenji Nakagawa (2015)

Applications of Mathematics

We give a sufficient condition for a non-negative random variable X to be of Pareto type by investigating the Laplace-Stieltjes transform of the cumulative distribution function. We focus on the relation between the singularity at the real point of the axis of convergence and the asymptotic decay of the tail probability. For the proof of our theorems, we apply Graham-Vaaler’s complex Tauberian theorem. As an application of our theorems, we consider the asymptotic decay of the stationary distribution...

Tame L p -multipliers

Kathryn Hare (1993)

Colloquium Mathematicae

We call an L p -multiplier m tame if for each complex homomorphism χ acting on the space of L p multipliers there is some γ 0 ∈ Γ and |a| ≤ 1 such that χ ( γ m ) = a m ( γ 0 γ ) for all γ ∈ Γ. Examples of tame multipliers include tame measures and one-sided Riesz products. Tame multipliers show an interesting similarity to measures. Indeed we show that the only tame idempotent multipliers are measures. We obtain quantitative estimates on the size of L p -improving tame multipliers which are similar to those obtained for measures, but...

The Affine Frame in p -adic Analysis

Ming Gen Cui, Huan Min Yao, Huan Ping Liu (2003)

Annales mathématiques Blaise Pascal

In this paper, we will introduce the concept of affine frame in wavelet analysis to the field of p -adic number, hence provide new mathematic tools for application of p -adic analysis.

The Bohr inequality for ordinary Dirichlet series

R. Balasubramanian, B. Calado, H. Queffélec (2006)

Studia Mathematica

We extend to the setting of Dirichlet series previous results of H. Bohr for Taylor series in one variable, themselves generalized by V. I. Paulsen, G. Popescu and D. Singh or extended to several variables by L. Aizenberg, R. P. Boas and D. Khavinson. We show in particular that, if f ( s ) = ∑ n = 1 ∞ a ₙ n - s with | | f | | ∞ : = s u p ℜ s > 0 | f ( s ) | < ∞ , then ∑ n = 1 ∞ | a ₙ | n - 2 ≤ | | f | | ∞ and even slightly better, and ∑ n = 1 ∞ | a ₙ | n - 1 / 2 ≤ C | | f | | ∞ , C being an absolute constant.

The Bohr-Pál theorem and the Sobolev space W ₂ 1 / 2

Vladimir Lebedev (2015)

Studia Mathematica

The well-known Bohr-Pál theorem asserts that for every continuous real-valued function f on the circle there exists a change of variable, i.e., a homeomorphism h of onto itself, such that the Fourier series of the superposition f ∘ h converges uniformly. Subsequent improvements of this result imply that actually there exists a homeomorphism that brings f into the Sobolev space W ₂ 1 / 2 ( ) . This refined version of the Bohr-Pál theorem does not extend to complex-valued functions. We show that if α < 1/2,...

The boundedness of Calderón-Zygmund operators on the spaces Fpα,q.

Michel Frazier, Rodolfo Torres, Guido Weiss (1988)

Revista Matemática Iberoamericana

Calderón-Zygmund operators are generalizations of the singular integral operators introduced by Calderón and Zygmund in the fifties [CZ]. These singular integrals are principal value convolutions of the formTf(x) = límε→0 ∫|x-y|&gt;ε K(x-y) f(y) dy = p.v.K * f(x),where f belongs to some class of test functions.

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