Mixed fractional integration operators

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The book delves into mixed Riemann Liouville integrals of functions with two variables, exploring Hölder spaces characterized by differing orders in each variable. It examines both first-order differences and mixed second-order differences, focusing on evaluating mixed fractional integrals. The findings extend the classical Hardy-Littlewood theorem from one-dimensional to mixed Hölderness scenarios, including considerations for weighted cases with power weights. This research contributes to the understanding of fractional calculus in higher dimensions and its applications.