Vector-valued singular integral operators on Morrey type spaces and variable Triebel–Lizorkin–Morrey spaces

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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. Copyright © 2012 Academia Scientiarum Fennica.
Original languageEnglish
Pages (from-to)375-406
JournalAnnales Academiæ Scientiarum Fennicæ Mathematica
Volume37
DOIs
Publication statusPublished - 2012

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Singular Integral Operator
Banach Function Space
Bounded Linear Operator
Decompose

Citation

Ho, K.-P. (2012). Vector-valued singular integral operators on Morrey type spaces and variable Triebel–Lizorkin–Morrey spaces. Annales Academiæ Scientiarum Fennicæ Mathematica, 37, 375-406.