Sharp weighted norm inequalities on MLpω for the Calderón Zygmund and Littlewood Paley operators are obtained in terms of the Ap characteristic of ω for any 1
Then, as main application of these estimates, we obtain a sharp Lp-norm estimate for the Bergman projection, which refines a result of K. Zhu as well as gives a negative answer to a question raised by M. Dostanić.
Our method is based on sharp estimates of norms of some outer functions, which allow us to transfer these problems to an estimate of the reproducing kernel of an appropriate weighted Sobolev space.
Especially, Chen in [2] obtained the sharp relationship between norm of the squared mean curvature and the warping function f of the warped product (M_{1}times _{f}M_{2}) isometrically immersed in a real space form, i.e., we have the following.
Moreover, in [9], Lerner obtained sharp (L^{p}_{w}) norm inequalities for the intrinsic square functions in terms of the (A_{p}) characteristic constant of w for all (1< p
For functions f on Rn satisfying certain conditions, we obtain sharp estimates of the operator norms (or norms in operator ideals) of f(A1,…,An)−f(B1,…,Bn) in terms of the corresponding norms of Aj−Bj, 1⩽j⩽n.
The sharp estimates of the norms of differences for the functions in Sobolev spaces have firstly been proved by Besov et al. [1, Volume 2, page 72].
In Section 3, under different norms, two sharp lower bounds of (D - A) are given for the low-rank approximation problem and some proofs of Theorem 3.5 are presented.
But those examples were in sharp opposition to the norm.
What happened then was a sharp deviation from the norm.
