A characterization of probability measures by f-moments

K. Urbanik

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Displaying similar documents to “A characterization of probability measures by f-moments”

Functionals on transient stochastic processes with independent increments

K. Urbanik (1992)

Studia Mathematica

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The paper is devoted to the study of integral functionals $ʃ_{0}^{\infty} f (X (t, ω)) d t$ for a wide class of functions f and transient stochastic processes X(t,ω) with stationary and independent increments. In particular, for nonnegative processes a random analogue of the Tauberian theorem is obtained.

Denseness of the spaces $Φ_{V}$ of Lizorkin type in the mixed $L^{p ̅} (ℝ^{n})$ -spaces

Stefan Samko (1995)

Studia Mathematica

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Stability of stochastic processes defined by integral functionals

K. Urbanik (1992)

Studia Mathematica

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The paper is devoted to the study of integral functionals $ʃ_{0}^{\infty} f (X (t, ω)) d t$ for continuous nonincreasing functions f and nonnegative stochastic processes X(t,ω) with stationary and independent increments. In particular, a concept of stability defined in terms of the functionals $ʃ_{0}^{\infty} f (a X (t, ω)) d t$ with a ∈ (0,∞) is discussed.

On the range of purely atomic probability measures

C. Ferens (1984)

Studia Mathematica

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Generalized convolutions V

K. Urbanik (1988)

Studia Mathematica

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Trigonometric sums associated with pseudo-measures

J. Benedetto (1971)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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$(H_{p}, L_{p})$ -type inequalities for the two-dimensional dyadic derivative

Ferenc Weisz (1996)

Studia Mathematica

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It is shown that the restricted maximal operator of the two-dimensional dyadic derivative of the dyadic integral is bounded from the two-dimensional dyadic Hardy-Lorentz space $H_{p, q}$ to $L_{p, q}$ (2/3 < p < ∞, 0 < q ≤ ∞) and is of weak type $(L_{1}, L_{1})$ . As a consequence we show that the dyadic integral of a ∞ function $f \in L_{1}$ is dyadically differentiable and its derivative is f a.e.

Two-sided estimates for the approximation numbers of Hardy-type operators in $L^{\infty}$ and L¹

W. Evans, D. Harris, J. Lang (1998)

Studia Mathematica

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In [2] and [3] upper and lower estimates and asymptotic results were obtained for the approximation numbers of the operator $T : L^{p} (ℝ^{+}) \to L^{p} (ℝ^{+})$ defined by $(T f) (x) ≔ v (x) ʃ_{0}^{\infty} u (t) f (t) d t$ when 1 < p < ∞. Analogous results are given in this paper for the cases p = 1,∞ not included in [2] and [3].

The converse of the Hölder inequality and its generalizations

Janusz Matkowski (1994)

Studia Mathematica

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Let (Ω,Σ,μ) be a measure space with two sets A,B ∈ Σ such that 0 < μ (A) < 1 < μ (B) < ∞ and suppose that ϕ and ψ are arbitrary bijections of [0,∞) such that ϕ(0) = ψ(0) = 0. The main result says that if $ʃ_{Ω} x y d μ \leq ϕ^{- 1} (ʃ_{Ω} ϕ \circ x d μ) ψ^{- 1} (ʃ_{Ω} ψ \circ x d μ)$ for all μ-integrable nonnegative step functions x,y then ϕ and ψ must be conjugate power functions. If the measure space (Ω,Σ,μ) has one of the following properties: (a) μ (A) ≤ 1 for every A ∈ Σ of finite measure; (b) μ (A) ≥ 1 for every A ∈ Σ of positive measure, then...