TY - JOUR
T1 - Inframonogenic decomposition of higher-order Lipschitz functions
AU - Abreu Blaya, Ricardo
AU - Alfonso Santiesteban, Daniel
AU - Bory Reyes, Juan
AU - Moreno García, Arsenio
N1 - Publisher Copyright:
© 2022 John Wiley & Sons, Ltd.
PY - 2022/6
Y1 - 2022/6
N2 - Euclidean Clifford analysis has become a well-established theory of monogenic functions in higher-dimensional Euclidean space with a variety of applications both inside and outside of mathematics. Noncommutativity of the geometric product in Clifford algebras leads to what are now known as inframonogenic functions, which are characterized by certain elliptic system associated to the orthogonal Dirac operator in (Formula presented.). The main question we shall be concerned with is whether or not a higher-order Lipschitz function on the boundary Γ of a Jordan domain (Formula presented.) can be decomposed into a sum of the two boundary values of a sectionally inframonogenic function with jump across Γ. To this end, a kind of Cauchy-type integral and singular integral operator, very specific to the inframonogenic setting, are widely used.
AB - Euclidean Clifford analysis has become a well-established theory of monogenic functions in higher-dimensional Euclidean space with a variety of applications both inside and outside of mathematics. Noncommutativity of the geometric product in Clifford algebras leads to what are now known as inframonogenic functions, which are characterized by certain elliptic system associated to the orthogonal Dirac operator in (Formula presented.). The main question we shall be concerned with is whether or not a higher-order Lipschitz function on the boundary Γ of a Jordan domain (Formula presented.) can be decomposed into a sum of the two boundary values of a sectionally inframonogenic function with jump across Γ. To this end, a kind of Cauchy-type integral and singular integral operator, very specific to the inframonogenic setting, are widely used.
KW - Clifford analysis
KW - higher-order Lipschitz class
KW - inframonogenic functions
UR - http://www.scopus.com/inward/record.url?scp=85122821833&partnerID=8YFLogxK
U2 - 10.1002/mma.8078
DO - 10.1002/mma.8078
M3 - Artículo
AN - SCOPUS:85122821833
SN - 0170-4214
VL - 45
SP - 4911
EP - 4928
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 9
ER -