Abstract
AbstractThis paper studies the relationship between vector-valued BMO functions and the Carleson measures defined by their gradients. Let dA and dm denote Lebesgue measures on the unit disc D and the unit circle 𝕋, respectively. For 1 < q < ∞ and a Banach space B, we prove that there exists a positive constant c such thatholds for all trigonometric polynomials f with coefficients in B if and only if B admits an equivalent norm which is q-uniformly convex, whereThe validity of the converse inequality is equivalent to the existence of an equivalent q-uniformly smooth norm.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
