Decomposition of weighted Triebel–Lizorkin and Besov spaces on the ball

By George Kyriazis, Pencho Petrushev, Yuan Xu. 2007

57 citations recorded by the source corpus.

Weighted Triebel–Lizorkin and Besov spaces on the unit ball Bd in ℝd with weights wμ(x)=(1−|x|2)μ−1/2, μ⩾0, are introduced and explored. A decomposition scheme is developed in terms of almost exponentially localized polynomial elements (needlets) {φξ}, {ψξ} and it is shown that the membership of a distribution to the weighted Triebel–Lizorkin or Besov spaces can be determined by the size of the needlet coefficients {〈f, φξ〉} in appropriate sequence spaces.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/95c090ab535005527f8035dc1904f9cbd97aeba3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Wavelet transforms for homogeneous mixed-norm Triebel–Lizorkin spaces (2016, background): “For spaces on other domains such as the sphere, see for example [18, 25, 26, 29, 30].”
Decomposition of Spaces of Distributions Induced by Hermite Expansions (2007, background): “art of a bigger project for needlet characterization of Triebel-Lizorkin and Besov spaces on nonclassical domains such as the unit sphere [10], the interval with Jacobi weights [7], and the unit ball [8]. The rest of the paper is organized as follows: Section 2 contains some background material. The”
Heat Kernel Generated Frames in the Setting of Dirichlet Spaces (2012, background): “the development of frames and weighted Besov and Triebel-Lizorkin spaces on the unit ball B in R in [36, 48], which perfectly fit in our general setting, but we shall not pursue in this article.”