Show simple item record

dc.creatorMartell, JM
dc.creatorMitrea, D
dc.creatorMitrea, I
dc.creatorMitrea, M
dc.date.accessioned2021-02-03T16:34:03Z
dc.date.available2021-02-03T16:34:03Z
dc.date.issued2016-01-01
dc.identifier.issn0213-2230
dc.identifier.doihttp://dx.doi.org/10.34944/dspace/5728
dc.identifier.otherEA8IS (isidoc)
dc.identifier.urihttp://hdl.handle.net/20.500.12613/5746
dc.description.abstract© 2016 European Mathematical Society. We show that the boundedness of the Hardy-Littlewood maximal operator on a Kothe function space X and on its Kothe dual X is equivalent to the well-posedness of the X-Dirichlet and X-Dirichlet problems in Rn + in the class of all second-order, homogeneous, elliptic systems, with constant complex coefficients. As a consequence, we obtain that the Dirichlet problem for such systems is well-posed for boundary data in Lebesgue spaces, variable exponent Lebesgue spaces, Lorentz spaces, Zygmund spaces, as well as their weighted versions. We also discuss a version of the aforementioned result which contains, as a particular case, the Dirichlet problem for elliptic systems with data in the classical Hardy space H1, and the Beurling-Hardy space HAp for p € (1,∞). Based on the well-posedness of the Lp-Dirichlet problem we then prove the uniqueness of the Poisson kernel associated with such systems, as well as the fact that they generate a strongly continuous semigroup in natural settings. Finally, we establish a general Fatou type theorem guaranteeing the existence of the pointwise nontangential boundary trace for null-solutions of such systems.
dc.format.extent913-970
dc.language.isoen
dc.relation.haspartRevista Matematica Iberoamericana
dc.relation.isreferencedbyEuropean Mathematical Society Publishing House
dc.subjectDirichlet problem
dc.subjectsecond-order elliptic system
dc.subjectnontangential maximal function
dc.subjectHardy-Littlewood maximal operator
dc.subjectPoisson kernel
dc.subjectGreen function
dc.subjectKothe function space
dc.subjectMuckenhoupt weight
dc.subjectLebesgue space
dc.subjectvariable exponent Lebesgue space
dc.subjectLorentz space
dc.subjectZygmund space
dc.subjectOrlicz space
dc.subjectHardy space
dc.subjectBeurling algebra
dc.subjectHardy-Beurling space
dc.subjectsemigroup
dc.subjectFatou type theorem
dc.titleThe Dirichlet problem for elliptic systems with data in Köthe function spaces
dc.typeArticle
dc.type.genreJournal Article
dc.relation.doi10.4171/rmi/903
dc.ada.noteFor Americans with Disabilities Act (ADA) accommodation, including help with reading this content, please contact scholarshare@temple.edu
dc.date.updated2021-02-03T16:34:00Z
refterms.dateFOA2021-02-03T16:34:04Z


Files in this item

Thumbnail
Name:
1405.3329v2.pdf
Size:
668.6Kb
Format:
PDF

This item appears in the following Collection(s)

Show simple item record