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Description: |
Our aim in this talk is to consider Besov-Morrey and Triebel-Lizorkin-Morrey spaces with variable exponents and present some of their properties, in particular the atomic and molecular representations. This reports on joint work with Alexandre Almeida (Besov-Morrey spaces) and Henning Kempka (Triebel-Lizorkin-Morrey spaces).
We plan to reach this objective in three parts.
In the first part we start by recalling what a (classical, constant exponents) Morrey space is and its connection with L_p-spaces. Then we recall what is meant by (classical, constant exponents) Besov and Triebel-Lizorkin spaces. Finally, we give the definition of Besov-Morrey and Triebel-Lizorkin-Morrey spaces, still assuming the exponents are constant.
In the second part we explain what is meant by spaces with variable exponents, starting with variable exponents Morrey spaces and going then to the Besov and Triebel-Lizorkin spaces with variable exponents.
In the third part of the talk we mix two of the previous ideas, finally presenting Besov-Morrey and Triebel-Lizorkin-Morrey spaces with variable exponents and exploring some of their properties.
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