The Zygmund condition for Bloch functions in the ball in 𝐶ⁿ

Abstract

In this paper we prove the equivalence of the Bloch condition for a holomorphic function <italic>f</italic> on the ball <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper B Subscript n"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>n</mml:mi> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{B_n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with the Zygmund second difference condition for a suitable primitive <italic>F</italic> of <italic>f</italic>.

Locations

• Proceedings of the American Mathematical Society - View - PDF