Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Some sharp weak-type inequalities for holomorphic functions on the unit ball of $ {\bf C}\sp n$

Author: Bogusław Tomaszewski
Journal: Proc. Amer. Math. Soc. 95 (1985), 271-274
MSC: Primary 32A35; Secondary 32A40
MathSciNet review: 801337
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ {B^n} = \{ z \in {{\mathbf{C}}^n}:\vert z\vert < 1\} $, $ {S^n} = \partial {B^n}$ and let $ {\sigma _n}$ be the Haar measure on $ {S^n}$. Then for all $ f \in {H^p}(1 \leqslant p < \infty )$ such that $ \operatorname{Im} (f(0)) = 0$ and $ t > 0$,

$\displaystyle {\sigma _n}(\{ z \in {S^n}:\vert f(z)\vert \geqslant t\} ) \leqslant {C_p} \cdot \frac{{\vert\vert\operatorname{Re} \,f\vert\vert _p^p}} {{{t^p}}}$

for some constant $ {C_p}$ depending only on $ p$. The best constant $ {C_p}$ is found for $ 1 \leqslant p \leqslant 2$.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32A35, 32A40

Retrieve articles in all journals with MSC: 32A35, 32A40

Additional Information

PII: S 0002-9939(1985)0801337-6
Article copyright: © Copyright 1985 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia