Harmonic Analysis on Spaces of Homogeneous Type

By D. Deng, Yongsheng Han, Yves Meyer. 2008

174 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7ae784801a0fbc2a06e445266386eed4b7cbe41d

How researchers see this paper

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

In Biomedical Engineering

1. Ji Li
2. Lesley A. Ward
3. Wen Yuan
4. Ronald R. Coifman
5. Boaz Nadler
6. Dachun Yang
7. Yongsheng Han

In Computational Theory and Mathematics

1. M. Mitrea
2. S. Hofmann
3. P. Auscher
4. D. Mitrea
5. Ronald R. Coifman
6. Ji Li
7. Lesley A. Ward
8. Loukas Grafakos

In Mathematical Physics

1. Dachun Yang
2. Wen Yuan
3. P. Auscher
4. Ji Li
5. S. Hofmann
6. Tuomas Hytönen
7. Liguang Liu
8. Loukas Grafakos

Citations in the corpus

• Multilinear analysis on metric spaces (2014, background): “This section provides necessary notions and results related to the spaces of homogeneous type and the so-called RD-spaces; see [22, 23, 76, 77, 27, 65, 62, 60, 61] and the references therein.”
• Hardy spaces associated with ball quasi‐Banach function spaces on spaces of homogeneous type: Characterizations of maximal functions, decompositions, and dual spaces (2021, background): “From then on, spaces of homogeneous type have become the most natural and the most general underlying space to study the real-variable theory of function spaces and the boundedness of operators (see, for instance, [16, 44, 47, 48, 53, 56]).”
• Multiparameter Hardy space theory on Carnot-Carathéodory spaces and product spaces of homogeneous type (2012, background): “3), the Littlewood-Paley-Stein theory and the Hardy space on (M,d, μ) have been established; see [10] for more details and the references therein.”
• Multiscale Wavelets on Trees, Graphs and High Dimensional Data: Theory and Applications to Semi Supervised Learning (2010, background): “Finally, from a mathematical viewpoint, the above construction of a probability measure and metric on a tree leads to a particular instance of an abstract object known in harmonic analysis as a Space of Homogeneous Type (Coifman & Weiss, 1977; Deng & Han, 2009).”
• $L^p$-Square Function Estimates on Spaces of Homogeneous Type and on Uniformly Rectifiable Sets (2013, background): “While this is a topic treated at some length in [25], [28], [36], we prove below a version of this result which best suits the purposes we have in mind.”
• A Complete Real-Variable Theory of Hardy Spaces on Spaces of Homogeneous Type (2018, unknown): “More on analysis over Ahlfors-n regular metric measure spaces or RD-spaces can be found in [18, 22, 33, 34, 52, 32, 55, 8, 56].”
• Orthonormal bases of regular wavelets in spaces of homogeneous type (2011, background): “Such a result is surely part of the folklore, but surprisingly difficult to find spelled out in complete generality: the seminal paper of David–Journé–Semmes [9] makes several assumptions on the space, like the small boundary property of balls, and many recent references treat other special cases li”
• Hardy space theory on spaces of homogeneous type via orthonormal wavelet bases (2015, methodology): “ley theory, and function spaces on (X,d′,µ) were developed in [H1], [HS] and [H2]. However, in those works wavelet bases were replaced by frames, which in many applications offer the same service; see [DH] for more details. In [NS1], Nagel and Stein developed the product Lp (1 <p<∞) theory in t”