Commutators of multiparameter flag singular integrals and applications
| Autor: | Yumeng Ou, Jill Pipher, Brett D. Wick, Ji Li, Xuan Thinh Duong |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
42B30 42B20 42B35 Mathematics::Classical Analysis and ODEs Hardy space 01 natural sciences Upper and lower bounds law.invention Riesz transform symbols.namesake multiparameter flag setting law 0103 physical sciences Classical Analysis and ODEs (math.CA) FOS: Mathematics flag commutator 42B30 0101 mathematics Mathematics::Representation Theory 42B35 Mathematics div-curl lemma Mathematics::Functional Analysis Numerical Analysis BMO space Applied Mathematics 010102 general mathematics Commutator (electric) Singular integral Harmonic function Mathematics - Classical Analysis and ODEs Iterated function symbols 010307 mathematical physics 42B20 Analysis Flag (geometry) |
| Zdroj: | Anal. PDE 12, no. 5 (2019), 1325-1355 |
| ISSN: | 1948-206X 2157-5045 |
| DOI: | 10.2140/apde.2019.12.1325 |
| Popis: | We introduce the iterated commutator for the Riesz transforms in the multi-parameter flag setting, and prove the upper bound of this commutator with respect to the symbol $b$ in the flag BMO space. Our methods require the techniques of semigroups, harmonic functions and multi-parameter flag Littlewood-Paley analysis. We also introduce the big commutator in this multi-parameter flag setting and prove the upper bound with symbol $b$ in the flag little-bmo space by establishing the "exponential-logarithmic" bridge between this flag little bmo space and the Muckenhoupt $A_p$ weights with flag structure. As an application, we establish the div-curl lemmas with respect to the appropriate Hardy spaces in the multi-parameter flag setting. 33 pages. Final version |
| Databáze: | OpenAIRE |
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