Landau-Kolmogorov and Gagliardo-Nirenberg Inequalities for Differential Operators in Lorentz Spaces


  • Vu Nhat Huy Department of Mathematics, Hanoi University of Science, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam
  • Ngoc Huy Nguyen



Lorentz Spaces, Fourier Transform, Landau-Kolmogorov Inequality, Gagliardo-Nirenberg Inequaly, Generalized Functions.


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||N? and ||f||N?, ||Dm(P(D)f)||N? as follows

||P(D)f||N? K1(E)||f||N? + K2(E)||Dm(P(D)f)||N?

for all E > 0, where ||.||N? is the norm in Lorentz spaces N?(R). The corresponding inequalities in Lp(Rn) is also obtained.


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How to Cite

Huy, V. N., & Nguyen, N. H. (2022). Landau-Kolmogorov and Gagliardo-Nirenberg Inequalities for Differential Operators in Lorentz Spaces. The Journal of the Indian Mathematical Society, 89(3-4), 317–332.