Sentence examples for non-negative function on from inspiring English sources

Let w be some Ap weight and enjoy reverse Hölder inequality, and let L="−Δ+V be a Schrödinger operator on Rn, where V∈L1loc(Rn) is a non-negative function on Rn.

Let f be a non-negative function on (mathbb{R}_) such that f is integrable and is uniformly continuous.

Proposition 6 Let I be an interval such that 0 ∈ I, and let f be a non-negative function on I.

Let p be a non-negative function on ([0,infty)) and let f and g be two differentiable functions having the same monotony on ([0,infty )).

Let f be a non-negative function on (tgeq0) such that f is integrable on (tgeq0) and is uniformly continuous on (tgeq0).

Hardy's famous inequality reads int_{0}^{infty} biggl( frac{1}{x} int_{0}^{x}f(t),dt biggr)^{p},dxleq biggl(frac{p}{p-1} biggr)^{p} int _{0}^{infty}f^{p}(x),dx,quad p>1, (1) where (f(x)) is a p-integrable non-negative function on ((0,infty)).

Let ƒ, g be measurable non-negative functions on R, and let \̄tf, ḡ be their equimeasurable symmetric decreasing rearrangements.

Let (0 < s < infty), and assume that w and ϕ are non-negative functions on ((0,infty)).

Let (0< s<1) and (0leq a < infty), and assume that w and ϕ are non-negative functions on ((0,infty)).

The family of all weight functions (also called just weights) on I, that is, locally integrable non-negative functions on ( 0, ∞ ), is denoted by W ( I ).

Note that (G s)=f(s)s-2pF s)) s-2pF sn-negatise function, increasing on ([0,infty)) and decreasing on ((-infunction