TY - JOUR
AU - Huy, Vu Nhat
AU - Nguyen, Ngoc Huy
PY - 2022/08/23
Y2 - 2022/12/02
TI - Landau-Kolmogorov and Gagliardo-Nirenberg Inequalities for Differential Operators in Lorentz Spaces
JF - The Journal of the Indian Mathematical Society
JA - JIMS
VL - 89
IS - 3-4
SE - Articles
DO - 10.18311/jims/2022/25986
UR - https://informaticsjournals.com/index.php/jims/article/view/25986
SP - 317-332
AB - <p>In this paper, we establish some Landau-Kolmogorov inequalities and Gagliardo-Nirenberg inequalities for di?erential operators generated by polynomials. We illustrate the relation between ||P(D)f||<sub>N?</sub> and ||f||N?, ||D<sup>m</sup>(P(D)f)||<sub>N?</sub> as follows</p><p>||P(D)f||<sub>N?</sub> K<sub>1</sub>(E)||f||<sub>N?</sub> + K<sub>2</sub>(E)||D<sup>m</sup>(P(D)f)||<sub>N?</sub></p><p>for all E > 0, where ||.||N? is the norm in Lorentz spaces N?(R). The corresponding inequalities in L<sup>p</sup>(R<sup>n</sup>) is also obtained.</p>
ER -