Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/1651

 Title: Mixed Fractional Integration Operators in Mixed Weighted Hölder Spaces Authors: Mamatov, TulkinSamko, Stefan Keywords: Functions of two VariablesRiemann-Liouville IntegralsMixed Fractional IntegralsMixed Finite DifferencesHölder 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 URI: http://hdl.handle.net/10525/1651 ISSN: 1311-0454 Appears in Collections: 2010

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