Factorization of Hausdorff Operators

Throughout this study, we will gain a deeper understanding of Hausdorff operators that are commonly used in operator theory. The Hausdorff matrices Gamma, Cesàro, and Hölder are factorized here to derive novel inequalities. Specifically, a factorization based on the Gamma operator has also been introduced for these three operators. In addition, the author introduces a factorization for the Hölder operator based on the Cesàro operator, which was previously discovered by famous mathematicians but this time is handled with an entirely different approach.