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On the atomic decomposition of 𝐻¹ and interpolation [PDF]

Proceedings of the American Mathematical Society, 1986
The author gives a basic proof of the atomic decomposition for functions f in \(H^ 1\) (of the upper half plane). He uses the nontangential maximal function Nf in this proof. Using the symmetric decreasing rearrangement \((NF)^*\) of the maximal function he obtains an estimate quality (''Peetre K-functional'') \[ K(f,t)=\inf \{\| g\|_{H^ 1}+t\| h\|_{L^{
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Fast atomic decomposition by the inhibition method [PDF]

Proceedings 15th International Conference on Pattern Recognition. ICPR-2000, 2002
A new algorithm is introduced which is related to matching pursuit but allows updating more than one coding coefficient per iteration: the updated coefficients correspond to mutually orthogonal elements of the dictionary. Coding experiments on natural images show that the new method achieves the same trade-off as matching pursuit between number of ...
Pece, Arthur, Petkov, Nikolay
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Homogeneous Besov Spaces on Stratified Lie Groups and Their Wavelet Characterization

Journal of Function Spaces and Applications, 2012
We establish wavelet characterizations of homogeneous Besov spaces on stratified Lie groups, both in terms of continuous and discrete wavelet systems.
Hartmut Führ, Azita Mayeli
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Degrees of randomized computability: decomposition into atoms

CoRR, 2021
In this paper we study structural properties of LV-degrees of the algebra of collections of sequences that are non-negligible in the sense that they can be computed by a probabilistic algorithm with positive probability. We construct atoms and infinitely divisible elements of this algebra generated by sequences, which cannot be Martin-Löf random and ...
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Continuous Characterizations of Besov-Lizorkin-Triebel Spaces and New Interpretations as Coorbits

Journal of Function Spaces and Applications, 2012
We give characterizations for homogeneous and inhomogeneous Besov-Lizorkin-Triebel spaces (H. Triebel 1983, 1992, and 2006) in terms of continuous local means for the full range of parameters.
Tino Ullrich
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WEIGHTED BESOV AND TRIEBEL–LIZORKIN SPACES ASSOCIATED WITH OPERATORS AND APPLICATIONS

Forum of Mathematics, Sigma, 2020
Let $X$ be a space of homogeneous type and $L$ be a nonnegative self-adjoint operator on $L^{2}(X)$ satisfying Gaussian upper bounds on its heat kernels.
HUY-QUI BUI, THE ANH BUI, XUAN THINH DUONG   +2 more
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Atomic decompositions for noncommutative martingales

Journal of Functional Analysis, 2023
We prove an atomic type decomposition for the noncommutative martingale Hardy space $\h_p$ for all ...
Zeqian Chen, Narcisse Randrianantoanina, Quanhua Xu   +2 more
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Organizing the atoms of the clique separator decomposition into an atom tree

Discrete Applied Mathematics, 2014
We define an atom tree of a graph as a generalization of a clique tree: its nodes are the atoms obtained by clique minimal separator decomposition, and its edges correspond to the clique minimal separators of the graph.Given a graph GG, we compute an atom tree by using a clique tree of a minimal triangulation HH of GG.
Berry, Anne, Pogorelcnik, Romain, Simonet, Geneviève   +2 more
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Atomic Energy Commission Reports [PDF]

, 1965
Quarterly progress report on metallurgy research operations at Hanford Atomic Products Operation in Richland ...
Westinghouse Electric Corporation. Atomic Power Division.
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Martingale Operators and Hardy Spaces with Continuous Time Generated by Them

Mathematics
In this paper, we introduce the martingale Hardy spaces and BMO spaces generated by an operator T in continuous time and establish the atomic decomposition theorem of the space HpT under the condition that T is predictable.
Zhiwei Hao, Jianlan Yue, Ferenc Weisz
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