Abstract
The fundamental result: for an arbitrary bounded, simply connected domain Ω in ℂ, the subspace Ln,m p(Ω) of the space Lp(Ω, σ) (σ is the plane Lebesgue measure, p ≥ 1), consisting of the (m, n)-analytic functions in Ω, is complemented in LP(Ω, σ) (a function f is said to be (m, n)-analytic if (∂m+n/∂¯Zm∂Zn)f=0 in Ω). Consequently, by virtue of a theorem of J. Lindenstrauss and A. Pelczyński, the space Ln,m P(Ω) is linearly homeomorphic to lP. In particular, for m=n=1 we obtain that the space of all harmonic LP-functions in Ω is complemented in LP(Ω, σ). This result has been known earlier only for smooth domains.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.