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In strictly pseudoconvex domains with smooth boundary, we prove a commutator relationship between admissible integral operators, as introduced by Lieb and Range, and smooth vector fields which are tangential at boundary points. This makes it possible to gain estimates for admissible operators in function spaces which involve tangential derivatives. Examples are given under with circumstances these can be transformed into genuine Sobolev- and Ck-estimates.
Lampert, Christoph H.. "Boundary regularity of admissible operators.." Publicacions Matemàtiques 49.1 (2005): 179-195. <http://eudml.org/doc/41558>.
@article{Lampert2005, abstract = {In strictly pseudoconvex domains with smooth boundary, we prove a commutator relationship between admissible integral operators, as introduced by Lieb and Range, and smooth vector fields which are tangential at boundary points. This makes it possible to gain estimates for admissible operators in function spaces which involve tangential derivatives. Examples are given under with circumstances these can be transformed into genuine Sobolev- and Ck-estimates.}, author = {Lampert, Christoph H.}, journal = {Publicacions Matemàtiques}, keywords = {Operadores integrales; Conmutadores; Campos vectoriales; integral operators; commutator relationship; -Neumann problem}, language = {eng}, number = {1}, pages = {179-195}, title = {Boundary regularity of admissible operators.}, url = {http://eudml.org/doc/41558}, volume = {49}, year = {2005}, }
TY - JOUR AU - Lampert, Christoph H. TI - Boundary regularity of admissible operators. JO - Publicacions Matemàtiques PY - 2005 VL - 49 IS - 1 SP - 179 EP - 195 AB - In strictly pseudoconvex domains with smooth boundary, we prove a commutator relationship between admissible integral operators, as introduced by Lieb and Range, and smooth vector fields which are tangential at boundary points. This makes it possible to gain estimates for admissible operators in function spaces which involve tangential derivatives. Examples are given under with circumstances these can be transformed into genuine Sobolev- and Ck-estimates. LA - eng KW - Operadores integrales; Conmutadores; Campos vectoriales; integral operators; commutator relationship; -Neumann problem UR - http://eudml.org/doc/41558 ER -
