M ATHEMATICS I NSTITUTE 2014 : 04 A New Proof of the Atomic Decomposition of Hardy Spaces

A New Proof of the Atomic Decomposition of Hardy Spaces

A new proof is given of the atomic decomposition of Hardy spaces Hp, 0 < p ≤ 1, in the classical setting on Rn. The new method can be used to establish atomic decomposition of maximal Hardy spaces in general and nonclassical settings.

I Nstitute for M Athematics and Its a Pplications

M ATHEMATICS I NSTITUTE 2014 : 01 Convex optimization on Banach Spaces IMI P REPRINT S ERIES R . A . DeVore and V . N . Temlyakov C OLLEGE OF A RTS AND S CIENCES

Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space X. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper bounds for the convergence rate of the proposed algorithms are given. These bounds depend on the smoothness of the objective function and the sparsity or compres...

0 Ja n 20 02 Hardy spaces and divergence operators on strongly Lipschitz domains

Let Ω be a strongly Lipschitz domain of Rn. Consider an elliptic second order divergence operator L (including a boundary condition on ∂Ω) and define a Hardy space by imposing the non-tangential maximal function of the extension of a function f via the Poisson semigroup for L to be in L1. Under suitable assumptions on L, we identify this maximal Hardy space with atomic Hardy spaces, namely with...

On a decomposition of Hardy--Hilbert's type inequality

In this paper, two pairs of new inequalities are given, which decompose two Hilbert-type inequalities.