Generalized Carleson Measure Spaces and Their Applications
We introduce the generalized Carleson measure spaces CMOrα,q that extend BMO. Using Frazier and Jawerth's φ-transform and sequence spaces, we show that, for α∈R and 0<p≤1, the duals of homogeneous Triebel-Lizorkin spaces Ḟpα,q for 1<q<∞ and 0<q≤1 are CMO(q'/p)-(q'/q)-α,q&...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/879073 |
| Summary: | We introduce the generalized Carleson measure spaces CMOrα,q that extend BMO. Using Frazier and Jawerth's φ-transform and sequence spaces, we show that, for α∈R and 0<p≤1, the duals of homogeneous Triebel-Lizorkin spaces Ḟpα,q for 1<q<∞ and 0<q≤1 are CMO(q'/p)-(q'/q)-α,q' and CMOr-α+(n/p)-n,∞ (for any r∈R), respectively. As applications, we give the necessary and sufficient conditions for the boundedness of wavelet multipliers and paraproduct operators acting on homogeneous Triebel-Lizorkin spaces. |
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| ISSN: | 1085-3375 1687-0409 |