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Multipliers of Fourier Transforms

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

Abstract

In this chapter weighted Triebel-Lizorkin spaces are defined in a general settiing. The two-weighted criteria for fractional and singular integrals derived in the previous chapters enable us to develop a new approach to the theory of multipliers of Fourier transforms. For (L p, L q) multipliers we establish two-weight estimates involving weight functions which do not necessarily belong to the class A p . It should be noted that the derived conditions are not only sufficient but also necessary for a whole class of multipliers under consideration.

Keywords

Weight Function Singular Integral Fourier Multiplier Finite Measure Fourier Image 
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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

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