Small Divisor problems and A_p weights with an application

2024/07/28 by Chanillo, Sagun
#35E05 #42B20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2407.19522

Abstract

We establish a link between Muckenhoupt A_p weights and a means to address small divisor problems. We use this link to obtain a quantitative version of the Ehrenpreis-Malgrange theorem of local solvability for constant coefficient PDE. We give an example as to how our theorem applies. In our quantitative version of the Ehrenpreis-Malgrange theorem, the loss of derivatives in the solvability estimate is measured in the scale of Sobolev spaces via the use of Muckenhoupt A_p weights. A part of our results are global in nature.

Related

• An Introduction To Small Divisors
• Fixed point theorems for small divisors problems
• Global solvability of the Laplace equation in weighted Sobolev spaces
• On the Capacities Associated with Local Muckenhoupt Weights
• Cutting the loss of derivatives for solvability under condition (psi)