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.
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© 2002 Springer Science+Business Media Dordrecht
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Edmunds, D.E., Kokilashvili, V., Meskhi, A. (2002). Multipliers of Fourier Transforms. In: Bounded and Compact Integral Operators. Mathematics and Its Applications, vol 543. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9922-1_9
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DOI: https://doi.org/10.1007/978-94-015-9922-1_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6018-1
Online ISBN: 978-94-015-9922-1
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