The norm of a bounded composition operator induced by a disc automorphism is estimated on weighted Hardy spaces H(β) in which the classical Hardy space is continuously embedded. The estimate obtained is accurate in the sense that it provides the exact norm for particular instances of the sequence β. As a by-product of our results, an estimate for the norm of any bounded composition operator on ...

In this paper, we introduce the property (h) on Banach lattices and present its characterization in terms of disjoint sequences. Then, an example is given to show that order-to-norm continuous operator may not be σ-order continuous. Suppose T:E→F order-bounded from Dedekind σ-complete lattice E into complete F. We prove T σ-order-to-norm if only both order weakly compact addition, can represent...

More generally, in the first claim we can replace the Lp(Q) norm with any norm || · || on F with the Riesz property, which is that |f | ≤ |g| (pointwise) implies ||f || ≤ ||g||. For the second claim, we can use any norm that has the Riesz property and for which the norm of the constant function f ≡ 1 is 1, which is clearly satisfied by Lp(Q) when Q is a probability measure. With these more gene...

Abstract. This paper studies L2 norm error estimates for the div least-squares method for which the associated homogeneous least-squares functional is equivalent to the H(div) × H1 norm for the respective dual and primal variables. Least-squares of this type for the second-order elliptic equations, elasticity, and the Stokes equations are an active area of research, and error estimates in the H...

In this paper some embedding theorems related to fractional integration and differentiation in harmonic mixed norm spaces h(p, q, α) on the half-space are established. We prove that mixed norm is equivalent to a “fractional derivative norm” and that harmonic conjugation is bounded in h(p, q, α) for the range 0 < p ≤ ∞, 0 < q ≤ ∞. As an application of the above, we give a characterization of h(p...

We prove some pinching results for the extrinsic radius of compact hypersurfaces in space forms. In the hyperbolic space, we show that if the volume of M is 1, then there exists a constant C depending on the dimension of M and the L-norm of the second fundamental form B such that the pinching condition tanh(R) < 1 ||H||∞ + C (where H is the mean curvature) implies that M is diffeomorphic to an ...

We obtain upper and lower bounds for the H" norm of the RLS (Recursive-Least-Squares) algorithm. The H" norm may be regarded aa the worst-case energy gain from the disturbances to the prediction errors, and is therefore a measure of the robustness of an algorithm to perturbations and model uncertainty. Our results allow one to compare the robustness of RLS compared to the LMS (Least-Mean-Square...

Several inviscid models in hydrodynamics and geophysics such as the incompressible Euler vorticity equations, the surface quasi-geostrophic equation and the Boussinesq equations are not known to have even local well-posedness in the corresponding borderline Sobolev spaces. Here H is referred to as a borderline Sobolev space if the L∞-norm of the gradient of the velocity is not bounded by the H-...

Solutions to the Cauchy problem for the one-dimensional cubic nonlinear Schrödinger equation on the real line are studied in Sobolev spaces H, for s negative but close to 0. For smooth solutions there is an a priori upper bound for the H norm of the solution, in terms of the H norm of the datum, for arbitrarily large data, for sufficiently short time. Weak solutions are constructed for arbitrar...

The Haagerup norm ‖ · ‖h on the tensor product A ⊗ B of two C∗-algebras A and B is shown to be Banach space equivalent to either the Banach space projective norm ‖ · ‖γ or the operator space projective norm ‖ · ‖∧ if and only if either A or B is finite dimensional or A and B are infinite dimensional and subhomogeneous. The Banach space projective norm and the operator space projective norm are ...