Skip to main content

Representation via ∂-equation

  • 306 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 1767)

Abstract

The Fefferman-Stein decomposition theorem for BMOA is to say that every BMOA-function f can be written as the sum f 1f 2 where f 1, f 2H and Ref jL∞(T). The main aim of this chapter is to extend this result to Q p, p ∈ (0,1). This aim will be realized via: introducing Q p(T), the non-holomorphic version of Q p; finding the Q p(T) ∩ L (T)-solutions to the ∂-equation; and presenting the Fefferman-Stein type decomposition for Q p. As certain applications of the ∂-equation, we give the corona theorems for both Q pH and Q p, and then show the interpolation theorem for Q pH .

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   39.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2001). Representation via ∂-equation. In: Xiao, J. (eds) Holomorphic Q Classes. Lecture Notes in Mathematics, vol 1767. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45434-9_7

Download citation

  • DOI: https://doi.org/10.1007/3-540-45434-9_7

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42625-7

  • Online ISBN: 978-3-540-45434-2

  • eBook Packages: Springer Book Archive