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The role of the contributions of bamboo to the different income groups is evaluated on the basis of data, for 1987 and 1997, from 46 households and by using Gini coefficients, relative and absolute inequality weights, and movements of households through different income groups.
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We prove a uniform two-weight inequality, with potential weights, for these means.
In [8] Caffarelli, Kohn and Nirenberg proved a rather general interpolation inequality with weights.
We introduce an Aharonov-Bohm type magnetic field on three-dimensional Heisenberg group and show this quadratic form satisfy an improved Hardy inequality with weights.
The purpose of this section is to establish reverse Hölder inequality of weights in the class (A_{p}^{n}(mu)) adapted to our general product measure μ.
In Section 2, we will establish the reverse Hölder inequality for weights ω in the class (A_{p}^{n}(mu)) adapted to our general product measure μ, which is not necessarily doubling with respect to the rectangles with sides parallel to the coordinate axes in (mathbb{R}^{n}).
The corresponding generalized Poincaré-type inequalities with weights are derived.
Similarly, using the reverse Hölder's inequality with weight [15] and (2.3) gives (2.6) and (2.7).
Due to discrete Cauchy-Schwarz inequality with weight coefficient, we have.
We obtain estimates for the composition and the form of inequalities with weights.
By Hölder's inequality with weight [22] and (3.2), we have the following: (3.5).
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