Products of Functions in $$\mathrm {BMO}({\mathcal X})$$ BMO ( X ) and $$H^1_\mathrm{at}({\mathcal X})$$ H at 1 ( X ) via Wavelets Over Spaces of Homogeneous Type

Products of Functions in $$\mathrm {BMO}({\mathcal X})$$ BMO ( X ) and... Let $$({\mathcal X},d,\mu )$$ ( X , d , μ ) be a metric measure space of homogeneous type in the sense of R. R. Coifman and G. Weiss and $$H^1_\mathrm{at}({\mathcal X})$$ H at 1 ( X ) be the atomic Hardy space. Via orthonormal bases of regular wavelets and spline functions recently constructed by P. Auscher and T. Hytönen, the authors prove that the product $$f\times g$$ f × g of $$f\in H^1_\mathrm{at}({\mathcal X})$$ f ∈ H at 1 ( X ) and $$g\in \mathrm {BMO}({\mathcal X})$$ g ∈ BMO ( X ) , viewed as a distribution, can be written into a sum of two bounded bilinear operators, respectively, from $$H^1_\mathrm{at}({\mathcal X})\times \mathrm {BMO}({\mathcal X})$$ H at 1 ( X ) × BMO ( X ) into $$L^1({\mathcal X})$$ L 1 ( X ) and from $$H^1_\mathrm{at}({\mathcal X}) \times \mathrm {BMO}({\mathcal X})$$ H at 1 ( X ) × BMO ( X ) into $$H^{\log }({\mathcal X})$$ H log ( X ) , which affirmatively confirms the conjecture suggested by A. Bonami and F. Bernicot (This conjecture was presented by Ky in J Math Anal Appl 425:807–817, 2015). Journal of Fourier Analysis and Applications Springer Journals

Products of Functions in $$\mathrm {BMO}({\mathcal X})$$ BMO ( X ) and $$H^1_\mathrm{at}({\mathcal X})$$ H at 1 ( X ) via Wavelets Over Spaces of Homogeneous Type

Loading next page...
Springer US
Copyright © 2016 by Springer Science+Business Media New York
Mathematics; Fourier Analysis; Signal,Image and Speech Processing; Abstract Harmonic Analysis; Approximations and Expansions; Partial Differential Equations; Mathematical Methods in Physics
Publisher site
See Article on Publisher Site


You’re reading a free preview. Subscribe to read the entire article.

DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches


Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.



billed annually
Start Free Trial

14-day Free Trial