SOME LANDAU-KOLMOGOROV TYPE INEQUALITIES FOR DIFFERENTIAL OPERATORS GENERATED BY POLYNOMIALS

被引：0

作者：

Vu Nhat Huy ^{[1
,2
]}

Nguyen Ngoc Huy ^{[3
]}

Chu Van Tiep ^{[4
]}

机构：

[1] Vietnam Natl Univ, Dept Math, Hanoi Univ Sci, 334 Nguyen Trai, Hanoi, Vietnam

[2] Thang Long Univ, Thang Long Inst Math & Appl Sci, Hanoi, Vietnam

[3] Thuyloi Univ, Dept Math, 175 Tay Son, Hanoi, Vietnam

[4] Univ Danang, Dept Math, Univ Sci & Educ, 459 Ton Duc Thang, Danang, Vietnam

来源：

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA | 2021年 / 58卷 / 02期

关键词：

L-p-spaces; Landau-Kolmogorov inequality; Fourier transform; DERIVATIVES;

D O I：

10.1556/012.2021.58.2.1497

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we establish some Landau-Kolmogorov type inequalities for differential operators generated by polynomials in the following form parallel to P(D)f parallel to(p) <= K-1(epsilon, P)parallel to f parallel to(q) + K-2(epsilon, m)parallel to D-m(P(D)f)parallel to(p) for all epsilon > 0, where 0 < q <= p <= infinity, and the differential operator P(D) is obtained from the polynomial P(x) by substituting x -> i partial derivative/partial derivative x. Moreover, the explicit form of K-1(epsilon, P) and K-2(epsilon, m) are given.

引用

页码：246 / 262

页数：17

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