COMPARISON OF THE CLASSICAL BMO WITH THE BMO SPACES ASSOCIATED WITH OPERATORS AND APPLICATIONS

By D. Deng, Xuan Thinh Duong, Adam S. Sikora, Lixin Yan. 2006

48 citations recorded by the source corpus.

Let L be a generator of a semigroup satisfying the Gaussian upper bounds. In this paper, we study further a new BMOL space associated with L which was intro- duced recently by Duong and Yan. We discuss applications of the new BMOL spaces in the theory of singular integration such as BMOL estimates and interpolation results for fractional powers, purely imaginary powers and spectral multipliers of self adjoint operators. We also demonstrate that the space BMOL might coincide with or might be essentially different from the classical BMO space.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/a3357129273510499982b279ae84c5a9e76051d3

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In Applied Mathematics

1. Lixin Yan
2. D. Deng
3. Liang Song
4. Chaoqiang Tan
5. Dachun Yang
6. Xuan Thinh Duong
7. Renjin Jiang
8. Yuan Zhou

Citations in the corpus

• Factorization for Hardy spaces and characterization for BMO spaces via commutators in the Bessel setting (2015, unknown): “As indicated in [11], BMOo(R+, dx) $ BMO(R+, dx).”
• Duality of Hardy and BMO spaces associated with operators with heat kernel bounds on product domains (2005, methodology): “For this choice of e -tL, the spaces H~c~ (IR) and BMO~(R) coincide with the classical Hardy space and BMO space, respectively, [4, 11 ], and [14].”
• Hardy spaces associated to operators satisfying Davies–Gaffney estimates and bounded holomorphic functional calculus☆ (2013, unknown): “[13] D.”
• Classes of Hardy spaces associated with operators, duality theorem and applications (2008, unknown): “To begin with, let us recall some basic facts about the Neumann Laplacian N on R, which was studied in [12].”