New inequalities similar to Hardy-Hilbert inequality and their applications.

Zhongxue, Lü; Hongzheng, Xie

Displaying similar documents to “New inequalities similar to Hardy-Hilbert inequality and their applications.”

A new Hilbert-type linear operator with a composite kernel and its applications.

Zhong, Wuyi (2010)

Journal of Inequalities and Applications [electronic only]

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Spectrum of the weighted Laplace operator in unbounded domains

Alexey Filinovskiy (2011)

Mathematica Bohemica

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We investigate the spectral properties of the differential operator $- r^{s} Δ$ , $s \geq 0$ with the Dirichlet boundary condition in unbounded domains whose boundaries satisfy some geometrical condition. Considering this operator as a self-adjoint operator in the space with the norm ${∥ u ∥}_{L_{2, s} (Ω)}^{2} = \int_{Ω} r^{- s} {| u |}^{2} d x$ , we study the structure of the spectrum with respect to the parameter $s$ . Further we give an estimate of the rate of condensation of discrete spectra when it changes to continuous.