Whitney Extension Problem for Fractional Sobolev Spaces and Besov Spaces

Author

• Han Li, CUNY Graduate CenterFollow

Date of Degree

6-2026

Document Type

Doctoral Dissertation

Degree Name

Doctor of Philosophy

Program

Mathematics

Advisor

Azita Mayeli

Committee Members

Arie Israel

Yunping Jiang

Vincent Martinez

Subject Categories

Analysis

Keywords

Whitney Extension, Jet Space, Fractional Sobolev Space, Besov Space

Abstract

In the dissertation, we go through the development of the Whitney extension problem and prove a type of results for the Whitney extension problem for homogeneous fractional Sobolev spaces and homogeneous Besov spaces.

This dissertation consists of four chapters:

Chapter 1: We recall the history of the Whitney extension problem and talk about some early works which have been done for the Whitney extension problem. We also mention our new results.

Chapter 2: We introduce some basic notations, definitions and preliminary results.

Chapter 3: We show the existence of a bounded linear extension operator for homogeneous fractional Sobolev space L^s,p(Rⁿ) when n/p is less than the fractional part of s. Our approach builds upon the classical Whitney extension operator and uses the method of exponentially decreasing paths.

Chapter 4: We extend our result from homogeneous fractional Sobolev spaces to homogeneous Besov spaces using the real interpolation method.

Recommended Citation

Li, Han, "Whitney Extension Problem for Fractional Sobolev Spaces and Besov Spaces" (2026). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/6618