The Journal of the Indian Mathematical Society

Open Access Open Access  Restricted Access Subscription Access
Open Access Open Access Open Access  Restricted Access Restricted Access Subscription Access

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


Affiliations
1 Department of Mathematics, Hanoi University of Science, Vietnam National University, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam, Viet Nam
     

   Subscribe/Renew Journal


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.


Keywords

Lorentz Spaces, Fourier Transform, Landau-Kolmogorov Inequality, Gagliardo-Nirenberg Inequaly, Generalized Functions.
Subscription Login to verify subscription
User
Notifications
Font Size



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

Abstract Views: 322  |  PDF Views: 0

Authors

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

Abstract


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.


Keywords


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

References





DOI: https://doi.org/10.18311/jims%2F2022%2F25986