The classic Poincaré inequality bounds the L-norm of a function, f , orthogonal to a given function g in a domain Ω, in terms of some L-norm of its gradient in Ω. Suppose we now remove a set Γ from Ω and concentrate our attention on Λ = Ω \ Γ. This new domain might not even be connected and hence no Poincaré inequality can generally hold for it. This is so even if the volume of Γ is arbitrarily...

in this paper we consider contact cr-warped product submanifolds of the type $m = n_ttimes_f n_perp$, of a nearly kenmotsu generalized sasakian space form $bar m(f_1‎, ‎f_2‎, ‎f_3)$ and by use of hopf's lemma we show that $m$ is simply contact cr-product under certain condition‎. ‎finally‎, ‎we establish a sharp inequality for squared norm of the second fundamental form and equality case i...

This paper considers local convergence of secant methods for a nonlinear system of equations. The well-known local convergence theory has been developed by Broyden, Dennis and Moré (1973). They used a norm inequality such that the difference between two vectors transformed by some matrix is bounded above by an order of one of the two. Instead, in the present paper, we use an inequality that bou...

Abstract. We study inequalities connecting a product of uniform norms of polynomials with the norm of their product. Generalizing Gel’fond-Mahler inequality for the unit disk and Kneser-Borwein inequality for the segment [−1, 1], we prove an asymptotically sharp inequality for norms of products of algebraic polynomials over an arbitrary compact set in plane. Applying similar techniques, we prod...

An anisotropic convex Lorentz-Sobolev inequality is established, which extends Ludwig, Xiao, and Zhang's result to any norm from Euclidean norm, and the geometric analogue of this inequality is given. In addition, it implies that the (anisotropic) Pólya-Szegö principle is shown.

We use Simonenko quantitative indices of an N -function Φ to estimate two parameters qΦ and QΦ in Orlicz function spaces L [0,∞) with Orlicz norm, and get the following inequality: BΦ BΦ−1 ≤ qΦ ≤ QΦ ≤ AΦ Aφ−1 , where AΦ and BΦ are Simonenko indices. A similar inequality is obtained in L[0, 1] with Orlicz norm.

We study inequalities connecting a product of uniform norms of polynomials with the norm of their product. Generalizing Gel’fond-Mahler inequality for the unit disk and Kneser-Borwein inequality for the segment [−1, 1], we prove an asymptotically sharp inequality for norms of products of algebraic polynomials over an arbitrary compact set in plane. Applying similar techniques, we produce a rela...

We convert a conjectured inequality from quantum information theory, due to He and Vidal, into a block matrix inequality and prove a very special case. Given n matrices Ai, i = 1, . . . , n, of the same size, let Z1 and Z2 be the block matrices Z1 := (AjA ∗ i ) n i,j=1 and Z2 := (A ∗ jAi) n i,j=1. Then the conjectured inequality is (||Z1||1 − TrZ1) + (||Z2||1 − TrZ2) ≤ ∑ i̸=j ||Ai||2||Aj ||2 ...

we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.