Abstract

Several Hardy-type inequalities with weights related to Baouendi–Grushinoperators

Highlights

  • The well-known Hardy inequality in Rn, n ≥ 3, asserts that for all u ∈ C0∞ (Rn) ∫ Rn |∇u|2 dx ≥ ( n − 2 2 )2 u2 |x|2 dx. (1.1)Though the constant ( n−2 )2 is sharp, equality in is never achieved by any function u ∈ H01 (Rn)

  • Our goal in this paper is to prove several Lp Hardy-type inequalities with more general and nonstandard weights associated to the Baouendi–Grushin-type operators ∆γ

  • Recall that the following weighted Hardy-type inequalities in the Euclidean setting were proved by Ghoussoub and Moradifam [10]: Let a, b > 0 and α, β, m be real numbers

Read more

Summary

Introduction

Laptev et al [18] recently established weighted Hardy inequalities for the quadratic form of the magnetic Baouendi–Grushin operator with Aharonov–Bohm-type magnetic field. Our goal in this paper is to prove several Lp Hardy-type inequalities with more general and nonstandard weights associated to the Baouendi–Grushin-type operators ∆γ. For this goal we shall mainly use a technique developed in [17]. Recall that the following weighted Hardy-type inequalities in the Euclidean setting were proved by Ghoussoub and Moradifam [10]: Let a, b > 0 and α, β, m be real numbers

If αβ
This shows that one can put w
This means that one can put w
Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.