Sentence examples for be a sublinear operator from inspiring English sources

Let T be a sublinear operator.

Let T be a sublinear operator, that is, | T ( f + g ) | ≤ | T f | + | T g |.

Let be a sublinear operator, and let be a real linear proper subspace of.

Let T Ω be a sublinear operator satisfying (1.1) and bounded on L p ( R n ) for p > 1.

Let T Ω, α be a sublinear operator T Ω satisfying (1.2) and bounded from L p ( R n ) to L q ( R n ).

Lemma 2.1 Let 1 < p < ∞, T Ω be a sublinear operator and satisfy (1.1) with Ω ∈ L s ( S n − 1 ).

It is clear that if is a sublinear operator, then must be a convex operator, but the converse is not true in general.

From this and T being a sublinear operator, it follows that begin{aligned}& varphi bigl( bigl{ mathcal{M}^{sharp}(Tf)>( C+1)lambda bigr}, lambda bigr) & quad levarphi bigl( bigl{ mathcal{M}^{sharp}(Tg)>Clambda bigr}, lambda bigr) +varphi bigl( bigl{ mathcal{M}^{sharp}(Th)>lambda bigr}, lambda bigr) & quad =varphi bigl( bigl{ mathcal{M}^{sharp}(Th)>lambda bigr}, lambda bigr).

holds for all non-negative and non-increasing g on ( 0, ∞ ) if and only if A : = sup t > 0 ν 2 ( t ) t ∫ 0 t ln ( 1 + t r ) d r ess sup 0 < τ < r ν 1 < ∞, and c ≈ A. Lemma 3.1 Let 1 < p < ∞, b ∈ CBMO p 2, λ, 0 < λ < 1 n and 1 p = 1 p 1 + 1 p 2, T Ω is a sublinear operator and satisfies (1.1) with Ω ∈ L s ( S n − 1 ).

An operator is called a sublinear operator, if for all and all real number, (2.8).

An operator T : X → Y is called a sublinear operator if it satisfies | T ( f + g ) | ≤ | T f | + | T g |, | T ( α f ) | ≤ | α | | T f |, where X is a martingale space, Y is a measurable function space.