A direct proof of Open image in new window

  • Akihito Uchiyama
Part of the Springer Monographs in Mathematics book series (SMM)


$$ \left| {\smallint _{{\text{R}}^n } f\left( x \right)g\left( x \right)dx} \right| \leqslant C\left( n \right)\left\| {N_1 u} \right\|_{L^1 } \left\| g \right\|_{BMO,} $$
where u is defined by (12.3) and
$$ f \in L^1 \cap L^\infty ,g \in {\text{BMO, and supp }}g{\text{ is compact}} $$
Since \( \left\| {N_1 u} \right\|_{L^1 } \) dominates \( \left\| f \right\|_{H^1 } \) by Theorems 4.1 and 9.3, we have already obtained (13.1). In this section, we give a direct proof of (13.1) by modifying the argument of L. Carleson [76] and by using the ideas in N. Th. Varopoulos [77], P. W. Jones [78] and J. B. Garnett-P. W. Jones [82].


Lebesgue Measure Algebraic Geometry Hardy Space Signed Measure Direct Proof 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Japan 2001

Authors and Affiliations

  • Akihito Uchiyama

There are no affiliations available

Personalised recommendations