Calderón reproducing formulas and new Besov spaces associated with operators
By H. Bui, Xuan Thinh Duong, Lixin Yan. 2012
81 citations recorded by the source corpus.
Abstract Let L be the generator of an analytic semigroup whose heat kernel satisfies an upper bound of Poisson type acting on L 2 ( X ) where X is a (possibly non-doubling) space of polynomial upper bound on volume growth. The aim of this paper is to introduce a new class of Besov spaces associated with the operator L so that when L is the Laplace operator −Δ or its square root − Δ acting on the Euclidean space R n , the new Besov spaces are equivalent to the classical Besov spaces. Depending on the choice of L, the new Besov spaces are natural settings for generic estimates for certain singular integral operators such as the fractional powers L α . Since our approach does not require the doubling volume property of the underlying space, it is applicable to any subset Ω of Euclidean spaces without any smoothness requirement on the boundary. We will also develop a number of Calderon reproducing formulas which play an important role in the theory of function spaces and are of independent interest. As an application, we study Besov spaces associated with Schrodinger operators with non-negative potentials satisfying reverse Holder estimates.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c1d40c72089177594d5404b52a012a72e7ba925f
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In Applied Mathematics
- T. Coulhon
- Frédéric Bernicot
- Gerard Kerkyacharian
- Ismaël F. Bailleul
- Xuan Thinh Duong
- The Anh Bui
- H. Bui
- Pencho Petrushev
In Mathematical Physics
- Frédéric Bernicot
- T. Coulhon
- Ismaël F. Bailleul
- Gerard Kerkyacharian
- Xuan Thinh Duong
- The Anh Bui
- H. Bui
- Pencho Petrushev
Citations in the corpus
- Heat Kernel Generated Frames in the Setting of Dirichlet Spaces (2012, methodology): “For another approach to Besov spaces under heat kernel estimates, but a polynomial upper bound on the volume instead of the volume doubling condition, see [7].”
- WEIGHTED BESOV AND TRIEBEL–LIZORKIN SPACES ASSOCIATED WITH OPERATORS AND APPLICATIONS (2020, background): “(iii) In [9], the authors introduced the theory of Besov spaces Ḃs,L p,q associated with an operator L satisfying Poisson estimates on metric spaces with a measure”
- Besov and Triebel-Lizorkin Spaces Associated to Hermite Operators (2015, background): “See for example [2,9,10,12] and the references therein.”
- Heat semigroup and singular PDEs (2015, methodology): “(We refer the reader to [10] and [36] for more details on the extension of the semigroup to distributions.”