A Łojasiewicz inequality in hypocomplex structures of $\mathbb {R}^2$
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- by Abdelhamid Meziani
- Proc. Amer. Math. Soc. 150 (2022), 3875-3887
- DOI: https://doi.org/10.1090/proc/16019
- Published electronically: May 20, 2022
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Abstract:
For a real analytic complex vector field $L$, in an open set of $\mathbb {R}^2$, with local first integrals that are open maps, we attach a number $\mu \ge 1$ (obtained through Łojasiewicz inequalities) and show that the equation $Lu=f$ has bounded solution when $f\in L^p$ with $p>1+\mu$. We also establish a similarity principle between the bounded solutions of the equation $Lu=Au+B\overline {u}$ (with $A,B\in L^p$) and holomorphic functions.References
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Bibliographic Information
- Abdelhamid Meziani
- Affiliation: Department of Mathematics, Florida International University, Miami, Florida 33199
- MR Author ID: 239413
- Email: meziani@fiu.edu
- Received by editor(s): August 16, 2021
- Received by editor(s) in revised form: November 3, 2021
- Published electronically: May 20, 2022
- Communicated by: Ryan Hynd
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 3875-3887
- MSC (2020): Primary 35C15; Secondary 35F05
- DOI: https://doi.org/10.1090/proc/16019
- MathSciNet review: 4446237