Search results for "Hardy spaces"

Inner functions and local shape of orthonormal wavelets

2011

Abstract Conditions characterizing all orthonormal wavelets of L 2 ( R ) are given in terms of suitable orthonormal bases (ONBs) related with the translation and dilation operators. A particular choice of the ONBs, the so-called Haar bases, leads to new methods for constructing orthonormal wavelets from certain families of Hardy functions. Inner functions and the corresponding backward shift invariant subspaces articulate the structure of these families. The new algorithms focus on the local shape of the wavelet.

Hardy-Orlicz Spaces of conformal densities

2014

We define and prove characterizations of Hardy-Orlicz spaces of conformal densities.

Hardy spaces and quasiconformal maps in the Heisenberg group

2023

We define Hardy spaces $H^p$, $00$ such that every $K$-quasiconformal map $f:B \to f(B) \subset \mathbb{H}^1$ belongs to $H^p$ for all $0<p<p_0(K)$. Second, we give two equivalent conditions for the $H^p$ membership of a quasiconformal map $f$, one in terms of the radial limits of $f$, and one using a nontangential maximal function of $f$. As an application, we characterize Carleson measures on $B$ via integral inequalities for quasiconformal mappings on $B$ and their radial limits. Our paper thus extends results by Astala and Koskela, Jerison and Weitsman, Nolder, and Zinsmeister, from $\mathbb{R}^n$ to $\mathbb{H}^1$. A crucial difference between the proofs in $\mathbb{R}^n$ and $\mathbb{…

Weighted Hardy Spaces of Quasiconformal Mappings

2019

We establish a weighted version of the $H^p$-theory of quasiconformal mappings.

Norm estimates for operators from Hp to ℓq

AbstractWe give upper and lower estimates of the norm of a bounded linear operator from the Hardy space Hp to ℓq in terms of the norm of the rows and the columns of its associated matrix in certain vector-valued sequence spaces.