17 citations · 36 across the 11 of their papers we have counts for
11 papers
The Dirac-Hardy and Dirac-Sobolev inequalities in
A. A. Balinsky, W. D. Evans, T. Umeda
Dirac-Sobolev and Dirac-Hardy inequalities in are established in which the spaces which feature in the classical Sobolev and Hardy inequalities are replaced by weak $L^…
Hardy's inequality and curvature
A. A. Balinsky, W. D. Evans, R. T. Lewis
A Hardy inequality of the form \[\int_{\tildeΩ} |\nabla f({\bf{x}})|^p d {\bf{x}} \ge (\frac{p-1}{p})^p \int_{\tildeΩ} \{1 + a(δ, \partial \tildeΩ)(\x)\}\frac{|f({\bf{x}})|^p}{δ({\…
Colorization of Natural Images via L1 Optimization
Nassir Mohammad, Alexander Balinsky
Natural images in the colour space YUV have been observed to have a non-Gaussian, heavy tailed distribution (called 'sparse') when the filter G(U)(r) = U(r) - sum_{s \in N(r)} w{(Y…
Dirac-Sobolev inequalities and estimates for the zero modes of massless Dirac operators
A. Balinsky, W. D. Evans, Y. Saito
The paper analyses the decay of any zero modes that might exist for a massless Dirac operator $H:= \ba \cdot (1/i) \bgrad + Q, $ where is -matrix-valued and of orde…
Improved Hardy-Sobolev inequalities
A. Balinsky, W. D. Evans, D. Hundertmark +1
The main result includes features of a Hardy-type inequality and an inequality of either Sobolev or Gagliardo-Nirenberg type. It is inspired by the method of proof of a recent impr…
Sobolev inequality for localization of pseudo-relativistic energy
A. A. Balinsky, A. E. Tyukov
In this article we present Sobolev-type inequalities for the localization of pseudo-relativistic energy.