EFFECT OF BAROTHERMAL TREATMENT ON THE CRYSTAL STRUCTURE OF A NICKEL ALLOY AS PROBED BY X-RAY DIFFRACTION
Russian Journal of Inorganic Chemistry. IAPC Nauka/Interperiodica. Том 52. 2007. С. 108-111
We consider the weighted Hardy inequality (∫0 ∞ (∫0 x f(t)dt)q u(x)dx)1/q ≤ C(∫0 ∞ f p(x)v(x)dx)1/p for the case 0 < q < p < ∝, p > 1. The weights u(x) and v(x) for which this inequality holds for all f (x) ≥ 0 may be characterized by the Mazya-Rosin or by the Persson-Stepanov conditions. In this paper, we show that these conditions are not unique and can be supplemented by some continuous scales of conditions and we prove their equivalence. The results for the dual operator which do not follow by duality when 0 < q < 1 are also given. © ELEMENT.