Singular integral operators and a ∂¯ -problem for (φ, ψ) -harmonic functions

Abstract:

This paper aims at proving the boundedness property of multidimensional singular integral operators associated with (φ, ψ) -harmonic functions, which are connected by the use of two orthogonal basis of the Euclidean space Rm. Besides, necessary and sufficient conditions for the solvability of the ∂¯ -problem for such (φ, ψ) -harmonic functions are described. The basic devices that make it possible to state and prove both results are borrowed from Clifford analysis.

Año de publicación:

2021

Keywords:

• ∂¯ -problem
• structural sets
• Clifford analysis
• Singular integral operator
• higher order Lipschitz classes

Fuente:

scopus