Dyadic Approach to Hypersingular Operators
Published:Dec 31, 2025 17:03
•1 min read
•ArXiv
Analysis
This paper develops a real-variable and dyadic framework for hypersingular operators, particularly in regimes where strong-type estimates fail. It introduces a hypersingular sparse domination principle combined with Bourgain's interpolation method to establish critical-line and endpoint estimates. The work addresses a question raised by previous researchers and provides a new approach to analyzing related operators.
Key Takeaways
- •Develops a real-variable and dyadic framework for hypersingular operators.
- •Introduces a hypersingular sparse domination principle.
- •Applies Bourgain's interpolation method.
- •Provides critical-line and endpoint estimates.
- •Addresses a question from previous research and offers a new analytical approach.
Reference
“The main new input is a hypersingular sparse domination principle combined with Bourgain's interpolation method, which provides a flexible mechanism to establish critical-line (and endpoint) estimates.”