Atomic and Subatomic Decompositions in Anisotropic Function Spaces

By Walter Farkas. 2000

62 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c133982acef16999d2f94b2439d182072a33adbb

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

1. Dachun Yang
2. Wen Yuan
3. Jun Liu
4. Long Huang
5. Dorothee D. Haroske
6. Marcin Bownik
7. Hans Triebel
8. Kwok-Pun Ho

In Mathematical Physics

1. Dachun Yang
2. Wen Yuan
3. Jun Liu
4. Dorothee D. Haroske
5. Long Huang
6. Marcin Bownik
7. I. Piotrowska
8. Hans Triebel

Citations in the corpus

• Wavelet Characterizations for Anisotropic Besov Spaces (2002, unknown): “Wavelet-type characterizations are studied in [15, 22, 30].”
• A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin-Triebel spaces with mixed norms (2017, unknown): “(6) ‖ aj | θs0+(1−θ)s1 q ‖ ≤ c ‖ aj | s0 ∞‖ ‖ aj | s1 ∞‖ holds for all complex sequences (aj)j∈N0 in s0 ∞ .”
• Atomic and molecular decompositions of anisotropic Besov spaces (2005, methodology): “The non-isotropic variants of Triebel-Lizorkin and Besov spaces for diagonal dilations have been studied by Besov, Il’in, and Nikol’skiı̆ [1], Schmeisser and Triebel [32,34,36], Dintelmann [15,16], and Farkas [17].”
• Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces (2005, methodology): “More recently, Farkas [21] obtained atomic decomposition for Besov and Triebel-Lizorkin spaces associated with the above anisotropy.”
• Anisotropic Triebel-Lizorkin spaces with doubling measures (2007, methodology): “The nonisotropic variants of Triebel-Lizorkin and Besov spaces for diagonal dilations have been studied by Besov et al [1], Schmeisser and Triebel [32, 33, 34, 35, 36], and Farkas [ 14 ].”
• A note on wavelet bases in function spaces (2004, background): “We refer to [9] and [5] and the literature mentioned there.”
• Atomic decompositions of function spaces with Muckenhoupt weights, and some relation to fractal analysis (2008, background): “It closely follows ideas presented in [12] (for the anisotropic, unweighted situation) and [48, Thm.”
• Atomic and Littlewood–Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications (2018, background): “For more progresses about this theory, we refer the reader to [5, 19, 23, 24, 39, 40, 41, 76, 77].”