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 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.

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 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 f ( a X ( t , ω ) ) d t with a ∈ (0,∞) is discussed.

( 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 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 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 ( + ) L p ( + ) defined by ( T f ) ( x ) v ( x ) ʃ 0 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 ϕ - 1 ( ʃ Ω ϕ x d μ ) ψ - 1 ( ʃ Ω ψ 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...