Fractional type operators in weighted generalized Hölder spaces.

Samko, S.G.; Mussalaeva, Z.U.

Displaying similar documents to “Fractional type operators in weighted generalized Hölder spaces.”

Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω

Karapetyants, Nikolai, Samko, Natasha (2004)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A16, 26A33, 46E15. There are known various statements on weighted action of one-dimensional and multidimensional fractional integration operators in spaces of continuous functions, such as weighted generalized Hölder spaces Hω0(ρ) of functions with a given dominant ω of their continuity modulus.

Existence and uniqueness of fractional differential equations with integral boundary conditions.

Wang, Taige, Xie, Feng (2008)

The Journal of Nonlinear Sciences and its Applications

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Positive solutions for boundary value problem of nonlinear fractional differential equation.

Qiu, Tingting, Bai, Zhanbing (2008)

The Journal of Nonlinear Sciences and its Applications

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An equation in the left and right fractional derivatives of the same order

B. Stanković (2008)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

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Kolmogorov type inequalities for hypersingular integrals with homogeneous characteristic.

Babenko, Vladislav F., Churilova, Mariya S. (2007)

Banach Journal of Mathematical Analysis [electronic only]

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Inclusion Properties for Certain Classes of Analytic Functions Involving a Family of Fractional Integral Operators

Kishore Prajapat, Jugal (2008)

Fractional Calculus and Applied Analysis

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2000 Math. Subject Classification: 30C45 A known family of fractional integral operators is used here to define some new subclasses of analytic functions in the open unit disk U. For each of these new function classes, several inclusion relationships are established.

On the boundedness of classical operators on weighted Lorentz spaces.

Rakotondratsimba, Y. (1998)

Georgian Mathematical Journal

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LP → LQ - Estimates for the Fractional Acoustic Potentials and some Related Operators

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.

Criteria of strong type two-weighted inequalities for fractional maximal functions.

Gogatishvili, A., Kokilashvili, V. (1996)

Georgian Mathematical Journal

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On the exponential integrability of fractional integrals on spaces of homogeneous type

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 $L^{1 / α}$ into a certain Orlicz space. This extends results of Trudinger [T], Hedberg [H], and Adams-Bagby [AB].

Weak solutions to differential equations with left and right fractional derivatives defined on $ℝ$

T. M. Atanacković, S. Pilipović, B. Stanković (2009)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

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On weighted inequalities for operators of potential type

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...