Anisotropic Hardy spaces and wavelets

By Marcin Bownik. 2003

240 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/2f7d0cb69b38edb7cda28d275c471f56fd95d9ea

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

Citations in the corpus

Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation (2017, background): “ X i∈N bν,k i Lp0(Rn) . eΩ k p0 − 1 p− M (f(ν)) 0 Lp(·),q(Rn) → as k → ∞. Here and hereafter, for any p ∈ (0,∞), Hp A (R n) denotes the anisotropic Hardy space introduced by Bownik in [10]. By this and the fact that, for any ν ∈ N, kgν,kk L∞(Rn) → 0 as k → −∞, we have N f (ν) − X k=−N gν,k+1 −g”
BOUNDEDNESS OF SINGULAR INTEGRALS IN HARDY SPACES ON SPACES OF HOMOGENEOUS TYPE (2009, background): “1 is the same as in [26] (see also [4]), namely, when η = {ηk}k∈N with ηk ≤ C2−k for k ∈ N, certain ∈ (0, θ] and constant C > 0, and K ∈ Dρ(∞, η), we verify that the kernel K of the operator T = S ◦ T ◦ S for ∈ N still belongs to Dρ(∞, η̃) with η̃ = {C̃2−k }k∈N, where C̃ > 0 is independent of and k.”
On the ¹–¹ boundedness of operators (2008, background): “Fortunately, if T is a Calder´on–Zygmund operator, then the uniform boundedness of T on (1 , ∞ )-atoms implies the boundedness from H 1 ( R n ) to L 1 ( R n ) (see, for instance, [11, Ch. 7.3, Lemma 1], [2, Ch. 1.9], [7, Ch. III.7] and [8, Thm 6.7.1]).”
Variable Anisotropic Hardy Spaces and Their Applications (2017, methodology): “Recall that the anisotropic Hardy space H A(R n) with p ∈ (0,∞) was first introduced by Bownik [6], which is a generalization of the parabolic Hardy space studied in [11].”
Pseudodifferential operators on mixed‐norm Besov and Triebel–Lizorkin spaces (2016, background): “We can compare the anisotropic distance with the Euclidean norm (see [11], [12]): There is a constant c1 ≥ 1 such that for every x ∈ Rn, c−1 1 |x |1/aM ≤ |x | a ≤ c1|x |1/am , when |x | a ≥ 1, (2.”
Variable Hardy Spaces (2012, background): “Givenp(·) ∈MP0, for everyf ∈ S ′ the following are equivalent: (1) there existsΦ ∈ S, ∫ Φ(x)dx 6= 0, such thatMΦ,0f ∈ L; (2) for all N > n/p0 + n + 1, MNf ∈ L; (3) f is a bounded distribution and N f ∈ L.”
Duality and interpolation of anisotropic Triebel–Lizorkin spaces (2008, background): “For the results about existence and non-existence of such wavelets we refer the reader to [3,7].”
Atomic and Littlewood–Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications (2018, background): “Indeed, via borrowing some ideas from the proof of Bownik et al. [11, Lemma 2.12], we establish a discrete Calderón reproducing formula (see Lemma 4.13 below) associated to the anisotropic homogeneous quasi-norm on Rn for distributions vanishing weakly at infinity, which was introduced by Folland a”
Boundedness of operators on Hardy spaces via atomic decompositions (2005, background): “example, in [9, Chapter III.7] or [10, Theorem 6.7.1] for convolution-type Calder´ on-Zygmund operators and in [ 1, Chapter 1.9 ] or [15, Lemma 1 in Chapter 7.3] for non-convolution operators.”
Atomic and molecular decompositions of anisotropic Besov spaces (2005, methodology): “Here, we will only list a few basic properties of quasi-norms ρA, which will be used subsequently. For more details we refer to [ 3 ,24].”