A note on the BMO and Calder\'{o}n-Zygmund estimate
Yuanyuan Lian, Kai Zhang
TL;DR
This paper provides a straightforward proof of the pointwise BMO estimate for Poisson's equation, and demonstrates how the Calderón-Zygmund estimate can be derived using interpolation and duality techniques.
Contribution
It introduces a simplified proof for the BMO estimate and connects it to the Calderón-Zygmund estimate through interpolation and duality methods.
Findings
Simplified proof of the pointwise BMO estimate for Poisson's equation
Derivation of Calderón-Zygmund estimate via interpolation and duality
Clarification of the relationship between BMO and Calderón-Zygmund estimates
Abstract
In this note, we give a simple proof of the pointwise BMO estimate for Poisson's equation. Then the Calder\'{o}n-Zygmund estimate follows by the interpolation and duality.
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Taxonomy
TopicsAdvanced Harmonic Analysis Research · Advanced Mathematical Physics Problems · Numerical methods in inverse problems