Skip to main content

Part of the book series: Mathematics and Its Applications ((MAEE,volume 41))

  • 510 Accesses

Résumé

Let x = (ξ1, ξ2, ⋯ ξ k ), y=(ŋ1, ŋ2, ⋯, ŋ k ), z=(ζ1, ζ2, ⋯ ζ k ), ⋯ denote points of the k-dimensional Euclidean space Ek. Here k ≥ 1 but only the case k ≥ 2 will be of interest. The space may also be treated as a vector space by identifying x with the vector joining the origin 0 = (0, ⋯, 0) with the point x. The rules for addition of vectors and for multiplying them by scalars are the usual ones, and the norm is defined by the formula

$$\left| x \right| = {{\left( {\xi _{1}^{2} + \xi _{2}^{2} + \cdot \cdot \cdot + \xi _{k}^{2}} \right)}^{{{{1} \left/ {2} \right.}}}}.$$

.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1989 Kluwer Academic Publishers

About this chapter

Cite this chapter

Calderön, A.P., Zygmund, A. (1989). On a Problem of Mihlin. In: Hulanicki, A., Wojtaszczyk, P., Żelazko, W. (eds) Selected Papers of Antoni Zygmund. Mathematics and Its Applications, vol 41. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1045-4_7

Download citation

  • DOI: https://doi.org/10.1007/978-94-009-1045-4_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-6962-5

  • Online ISBN: 978-94-009-1045-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics