On the analytic version of the Mitiagin-DeLeeuw-Mirkhil non-inequality on bi-disc

TL;DR

This paper proves an analytic version of a non-inequality for complex partial differential operators on bi-discs, using Rudin-Shapiro polynomials, advancing understanding in complex analysis and PDEs.

Contribution

It introduces a novel proof of the analytic non-inequality for PDEs on bi-discs utilizing Rudin-Shapiro polynomials, which was not previously established.

Findings

Established the analytic version of the Mitiagin-DeLeeuw-Mirkhil non-inequality.

Applied Rudin-Shapiro polynomials to PDE analysis on bi-discs.

Provided new techniques for complex PDE inequalities.

Abstract

Using the method of Rudin-Shapiro polynomials we prove the analytic version of the Mitiagin-DeLeeuw-Mirkhil non-inequality for complex partial differential operators with constant coefficients on bi-disc.