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Title: Mixed Fractional Integration Operators in Mixed Weighted Hölder Spaces
Authors: Mamatov, Tulkin
Samko, Stefan
Keywords: Functions of two Variables
Riemann-Liouville Integrals
Mixed Fractional Integrals
Mixed Finite Differences
Hölder Spaces of Mixed Order
Issue Date: 2010
Publisher: Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation: Fractional Calculus and Applied Analysis, Vol. 13, No 3, (2010), 245p-260p
Abstract: We study mixed Riemann-Liouville integrals of functions of two variables in Hölder spaces of different orders in each variables. We consider Hölder spaces defined both by first order differences in each variable and also by the mixed second order difference, the main interest being in the evaluation of the latter for the mixed fractional integral in both the cases where the density of the integral belongs to the Hölder class defined by usual or mixed differences. The obtained results extend the well known theorem of Hardy-Littlewood for one-dimensional fractional integrals to the case of mixed Hölderness. We cover also the weighted case with power weights.
Description: MSC 2010: 26A33
ISSN: 1311-0454
Appears in Collections:2010

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