TY - JOUR
T1 - Singular integral operators and a ∂¯ -problem for (φ, ψ) -harmonic functions
AU - Ricardo, José Luis Serrano
AU - Reyes, Juan Bory
AU - Blaya, Ricardo Abreu
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2021/12
Y1 - 2021/12
N2 - 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.
AB - 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.
KW - Clifford analysis
KW - Higher order Lipschitz classes
KW - Singular integral operator
KW - Structural sets
KW - ∂¯ -problem
UR - http://www.scopus.com/inward/record.url?scp=85113157634&partnerID=8YFLogxK
U2 - 10.1007/s13324-021-00590-5
DO - 10.1007/s13324-021-00590-5
M3 - Artículo
AN - SCOPUS:85113157634
SN - 1664-2368
VL - 11
JO - Analysis and Mathematical Physics
JF - Analysis and Mathematical Physics
IS - 4
M1 - 155
ER -