Browsing by Author "Apseit K."

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    FACTORIZATIONS AND HARDY TYPE INEQUALITIES
    (Faculty of Engineering and Natural Science, 2024) Apseit K.
    In this thesis, we derive the Hardy and critical Hardy inequalities using any homogeneous quasi-norm in a unified way. Specifically, we establish a sharp remainder formula for these inequalities. Our identity extend to Hardy and critical Hardy inequalities for the radial derivative operator with any homogeneous quasi-norm, offering enhanced versions of classical results. Our approach is based on the factorization method of differential operators introduced by Gesztesy and Littlejohn. As an application, we show Caffarelli-Kohn-Nirenberg type inequalities with more general weight. Because of the freedom in the choice of any homogeneous quasi-norm, our results give new insights already in both anisotropic R n and isotropic R n . Our results not only generalize existing inequalities but also uncover new perspectives in the study of partial differential equations and functional inequalities. These advances could have significant implications for theoretical research and applications in which anisotropic and isotropic properties are relevant.