Fractional type operators in weighted generalized Hölder spaces.
Samko, S.G., Mussalaeva, Z.U. (1994)
Georgian Mathematical Journal
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Samko, S.G., Mussalaeva, Z.U. (1994)
Georgian Mathematical Journal
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Shiying Zhao (1996)
Colloquium Mathematicae
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In this paper, we discuss a class of weighted inequalities for operators of potential type on homogeneous spaces. We give sufficient conditions for the weak and strong type weighted inequalities sup_{λ>0} λ|{x ∈ X : |T(fdσ)(x)|>λ }|_{ω}^{1/q} ≤ C (∫_{X} |f|^{p}dσ)^{1/p} and (∫_{X} |T(fdσ)|^{q}dω )^{1/q} ≤ C (∫_X |f|^{p}dσ )^{1/p} in the cases of 0 < q < p ≤ ∞ and 1 ≤ q < p < ∞, respectively, where T is an operator of potential type, and ω and σ are Borel measures on...
Rakotondratsimba, Y. (1998)
Georgian Mathematical Journal
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Gogatishvili, A., Kokilashvili, V. (1996)
Georgian Mathematical Journal
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Rafeiro, Humberto, Samko, Stefan (2005)
Fractional Calculus and Applied Analysis
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2000 Mathematics Subject Classification: 26A33, 42B20 There is given a generalization of the Marchaud formula for one-dimensional fractional derivatives on an interval (a, b), −∞ < a < b ≤ ∞, to the multidimensional case of functions defined on a region in R^n
Kilbas, Anatoly, Sebastian, Nicy (2010)
Fractional Calculus and Applied Analysis
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Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09 Two integral transforms involving the Gauss-hypergeometric function in the kernels are considered. They generalize the classical Riemann-Liouville and Erdélyi-Kober fractional integral operators. Formulas for compositions of such generalized fractional integrals with the product of Bessel functions of the first kind are proved. Special cases for...
Kilbas, Anatoly (2005)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 26A33, 33C20. The paper is devoted to the study of the fractional calculus of the generalized Wright function pΨq(z) defined for z ∈ C, complex ai, bj ∈ C and real αi, βj ∈ R (i = 1, 2, · · · p; j = 1, 2, · · · , q) by the series pΨq (z) It is proved that the Riemann-Liouville fractional integrals and derivative of the Wright function are also the Wright functions but of greater order. Special cases are considered. * The present...
Genebashvili, I., Gogatishvili, A., Kokilashvili, V. (1996)
Georgian Mathematical Journal
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Atanackovic, T., Stankovic, B. (2004)
Fractional Calculus and Applied Analysis
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An expansion formula for fractional derivatives given as in form of a series involving function and moments of its k-th derivative is derived. The convergence of the series is proved and an estimate of the reminder is given. The form of the fractional derivative given here is especially suitable in deriving restrictions, in a form of internal variable theory, following from the second law of thermodynamics, when applied to linear viscoelasticity of fractional derivative type. ...
Karapetyants, Alexey, Karasev, Denis, Nogin, Vladimir (2005)
Fractional Calculus and Applied Analysis
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Mathematics Subject Classification: 47B38, 31B10, 42B20, 42B15. We obtain the Lp → Lq - estimates for the fractional acoustic potentials in R^n, which are known to be negative powers of the Helmholtz operator, and some related operators. Some applications of these estimates are also given. * This paper has been supported by Russian Fond of Fundamental Investigations under Grant No. 40–01–008632 a.
A. Gatto, Stephen Vági (1993)
Colloquium Mathematicae
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In this paper we show that the fractional integral of order α on spaces of homogeneous type embeds into a certain Orlicz space. This extends results of Trudinger [T], Hedberg [H], and Adams-Bagby [AB].