Mixed Fractional Integration Operators in Mixed Weighted Hölder Spaces

Mamatov, Tulkin, and Samko, Stefan. "Mixed Fractional Integration Operators in Mixed Weighted Hölder Spaces." Fractional Calculus and Applied Analysis 13.3 (2010): 245-260. <http://eudml.org/doc/219543>.

@article{Mamatov2010,
abstract = {MSC 2010: 26A33We 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.},
author = {Mamatov, Tulkin, Samko, Stefan},
journal = {Fractional Calculus and Applied Analysis},
keywords = {Functions of two Variables; Riemann-Liouville Integrals; Mixed Fractional Integrals; Mixed Finite Differences; Hölder Spaces of Mixed Order; functions of two variables; Riemann-Liouville integrals; mixed fractional integrals; mixed finite differences; Hölder spaces of mixed order},
language = {eng},
number = {3},
pages = {245-260},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Mixed Fractional Integration Operators in Mixed Weighted Hölder Spaces},
url = {http://eudml.org/doc/219543},
volume = {13},
year = {2010},
}

TY - JOUR
AU - Mamatov, Tulkin
AU - Samko, Stefan
TI - Mixed Fractional Integration Operators in Mixed Weighted Hölder Spaces
JO - Fractional Calculus and Applied Analysis
PY - 2010
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 13
IS - 3
SP - 245
EP - 260
AB - MSC 2010: 26A33We 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.
LA - eng
KW - Functions of two Variables; Riemann-Liouville Integrals; Mixed Fractional Integrals; Mixed Finite Differences; Hölder Spaces of Mixed Order; functions of two variables; Riemann-Liouville integrals; mixed fractional integrals; mixed finite differences; Hölder spaces of mixed order
UR - http://eudml.org/doc/219543
ER -