Skip to main content

Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 152))

  • 1128 Accesses

Abstract

This chapter treats two topics for which no reasonable home could be found elsewhere. Section 43, dealing with maximal functions in Lp (G), is of interest in its own right. Section 44, which explores pointwise summability of Fourier transforms on groups, is of interest as an extension of the classical theorem of Fejér and Lebesgue, and is also used in an essential way in Theorem (36.18) supra.

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 109.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • FejÉR, Leopold; [1] Untersuchungen über Fouriersche Reihen. Math. Ann. 58, 51–69 (1904).

    Article  MATH  Google Scholar 

  • Lebesgue, Henri; [2] Recherches sur la convergence des séries de Fourier. Math. Ann. 61, 251–280 (1905).

    Article  MathSciNet  MATH  Google Scholar 

  • Lebesgue, Henri; [3] Leçons sur les séries trigonométriques. Collection de Monographies sur la théorie des fonctions. Paris; Gauthier-Villars 1906.

    Google Scholar 

  • Saks, Stanislaw, and Antoni Zygmund; [1] Analytic functions, English edition. Monografie Matematyczne, Tom Xxviii. Warszawa.Wroclaw; 1952.

    Google Scholar 

  • Collins, H. S., and W. H. Summers; [1] Some applications of Hewitt’s factorization theorem. Proc. Amer. Math. Soc. 21, 727–733 (1969).

    MathSciNet  MATH  Google Scholar 

  • Yano, Shigeki; [1] On Walsh-Fourier series. T8hoku Math. J. (2) 3, 223–242 (1951).

    Article  MATH  Google Scholar 

  • Phillips, Keith L.: [1] Maximal functions for a class of locally compact non-compact groups. Bull. Amer. Math. Soc. 75, 384–386 (1969).

    Article  MathSciNet  MATH  Google Scholar 

  • Collins, H. S., and W. H. Summers; [1] Some applications of Hewitt’s factorization theorem. Proc. Amer. Math. Soc. 21, 727–733 (1969).

    MathSciNet  MATH  Google Scholar 

  • Cowman, R. R.: [1] Remarks on weak type inequalities for operators commuting with translations. Bull. Amer. Math. Soc. 74, 710–714 (1968).

    Article  MathSciNet  Google Scholar 

  • Ross, Kenneth A., and Karl Stromberg; [1] Jessen’s theorem On Riemann sums for locally compact groups. Pacific J. Math. 20, 135–147 (1967).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1970 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Hewitt, E., Ross, K.A. (1970). Miscellany. In: Abstract Harmonic Analysis. Grundlehren der mathematischen Wissenschaften, vol 152. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-26755-4_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-26755-4_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-24595-8

  • Online ISBN: 978-3-662-26755-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics