On fourier multipliers in weighted Triebel–Lizorkin spaces
<p/> <p>The paper is devoted to two-weighted estimates for multipliers of Fourier transforms. Apparently this problem has not been studied before. Easy to verify conditions for the pairs of weights ensuring two-weight estimates for several classes of multipliers in Triebel–Lizo...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2002-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/7/942837 |
| Summary: | <p/> <p>The paper is devoted to two-weighted estimates for multipliers of Fourier transforms. Apparently this problem has not been studied before. Easy to verify conditions for the pairs of weights ensuring two-weight estimates for several classes of multipliers in Triebel–Lizorkin spaces are derived. 'Ikvo-weighted boundedness criteria for the Riemann–Liouville and Weyl transforms on the line are established. The authors' recent results on trace inequalities for one-sided potentials in the "diagonal" case <inline-formula><graphic file="1029-242X-2002-942837-i1.gif"/></inline-formula> are applied. </p> <p>The method of proof consists of the representation of the operators under consideration in the form of compositions of certain "elementary" transformations.</p> <p>Various examples of pairs of weights governing two-weighted estimates for Fourier multipliers are presented.</p> |
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| ISSN: | 1025-5834 1029-242X |