| Abstract: |
| Function spaces with spatially heterogeneous behaviour have become an important tool in modern analysis. In this talk, I will discuss derivative-free descriptions of smoothness in the framework of variable exponent and generalized Orlicz spaces. The approach considered has its origins in the work of Bourgain, Brezis and Mironescu [2002, J. Anal. Math.] where difference quotients were used to study classical Sobolev spaces. In the setting of variable exponent and generalized Orlicz spaces, difference quotients are no longer adequate. It will be shown that the averaging operator introduced by Diening and Hasto [2007, Studia Math.] to address the trace space appropriately captures the desired smoothness of functions in a variable exponent Sobolev space as well as in a generalized Orlicz-Sobolev space. |
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