Advertisement

One-Sided Maximal Functions

  • David E. Edmunds
  • Vakhtang Kokilashvili
  • Alexander Meskhi
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 543)

Abstract

This chapter partly deals with one-sided fractional maximal functions and their various generalizations, among them one-sided maximal functions of Hörmander type. We establish L p L p v (1 < pq < ∞) boundedness criteria which are very easy to verify. The proofs depend heavily on the results on the Riemann-Liouville operator which were derived in the previous chapter. Then follows a study, from the point of view of boundedness and compactness, of potentials on the line, or on a bounded interval, involving power-logarithmic kernels and their multidimensional analogues as well.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • David E. Edmunds
    • 1
  • Vakhtang Kokilashvili
    • 1
  • Alexander Meskhi
    • 2
  1. 1.Centre for Mathematical Analysis and its ApplicationUniversity of SussexSussexUK
  2. 2.A. Razmadze Mathematical InstituteGeorgian Academy of SciencesTbilisiGeorgia

Personalised recommendations