General weighted Hardy-type inequalities related to greiner operators

Küçük Resim Yok

Tarih

2018

Dergi Başlığı

Dergi ISSN

Cilt Başlığı

Yayıncı

Rocky Mountain Mathematics Consortium

Erişim Hakkı

info:eu-repo/semantics/closedAccess

Özet

In this article, we present a general method that can be used to deduce weighted Hardy-type inequalities from a particular non-linear partial differential inequality in a relatively simple and unified way on the sub-Riemannian manifold R 2 n +1 = R n ×R n ×R, defined by the Greiner vector fields ? X j = ?xj + 2ky j |z| 2 k? 2 ? ?l , ? Y j = ?yj ? 2kx j |z| 2 k? 2 ? ?l , j = 1, . . ., n, where z = x + iy ? C n , l ? R, k ? 1. Our method allows us to improve, extend, and unify many previously obtained sharp weighted Hardy-type inequalities as well as to yield new ones. These cases are illustrated by giving many concrete examples, including radial, logarithmic, hyperbolic and non-radial weights. Furthermore, we introduce a new technique for constructing two-weight L p Hardy-type inequalities with remainder terms on smooth bounded domains ? in R 2 n +1 . We also give several applications leading to various weighted Hardy inequalities with remainder terms. Copyright © 2018 Rocky Mountain Mathematics Consortium.

Açıklama

Anahtar Kelimeler

Generalized Greiner operator, Heisenberg-Pauli-Weyl inequality, Remainder terms, Two-weight Hardy inequality, Weighted Hardy inequality

Kaynak

Rocky Mountain Journal of Mathematics

WoS Q Değeri

Q4

Scopus Q Değeri

Q2

Cilt

48

Sayı

7

Künye