On the Mellin symbol of singular integral operators associated with the biharmonic equation in infinite sectors

Authors

Jeongsu Kyeong, Syracuse University
Irina Mitrea, College of Science and Technology
Katharine A. Ott, Bates CollegeFollow

Publication Title

Contemporary Mathematics

Document Type

Book Chapter

Department or Program

Mathematics

Publication Date

2025

Keywords

beta function, Bilaplacian, Ferrers function, gamma function, Hardy kernels, hypergeometric function, jump formulas, Neumann problem, nontangential maximal function, nontangential trace, special functions

Abstract

This paper is concerned with the study of singular integral operators associated with the Neumann problem for the bi-Laplacian in infinite sectors in the plane. The main goal is to explicitly describe the Mellin symbol of such singular integral operators for arbitrary apertures θ ∈ (0, 2π) and Poisson ratios η ∈ [−1, 1). The analysis carried out here uses Mellin transform techniques and properties of hypergeometric functions of gamma, beta, Ferrers and Gauss type. The explicit Mellin symbol formulas open the door to obtaining information on the range of integrability exponents p ∈ (1,∞) for which the Neumann problem for Δ² is well-posed in this geometric setting.

Comments

Original version is available from the publisher at: https://doi.org/10.1090/conm/819/16389

Recommended Citation

Jeongsu K., Mitrea I., & Ott K. A. (2025). On the Mellin symbol of singular integral operators associated with the biharmonic equation in infinite sectors. In Maier, R. S., Cohl, H. S., & Costas-Santos, R. S. (eds.) Applications and $q$-Extensions of Hypergeometric Functions (Vol. 819). American Mathematical Society.