Annales Academię Scientiarum Fennicę
Mathematica
Volumen 37, 2012, 375-406
The Hong Kong Institute of Education, Department of Mathematics and Information Technology
10, Lo Ping Road, Tai Po, Hong Kong, China; vkpho 'at' ied.edu.hk
Abstract. A criteria on the vector-valued Banach function spaces X(B) is obtained so that whenever a vector-valued singular integral operator is bounded on X(B), it can be extended to be a bounded linear operator on the corresponding Morrey type spaces. Using this result, we define the generalized Triebel-Lizorkin-Morrey spaces and obtain the atomic and molecular decompositions. As a particular example of the generalized Triebel-Lizorkin-Morrey spaces, we introduce and study the variable Triebel-Lizorkin-Morrey spaces.
2010 Mathematics Subject Classification: Primary 42B20, 42B25, 42B35; Secondary 46E30, 46E40.
Key words: Vector-valued singular integral operators, Morrey spaces, Triebel-Lizorkin-Morrey spaces, variable exponent analysis.
Reference to this article: K.-P. Ho: Vector-valued singular integral operators on Morrey type spaces and variable Triebel-Lizorkin-Morrey spaces. Ann. Acad. Sci. Fenn. Math. 37 (2012), 375-406.
doi:10.5186/aasfm.2012.3746
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