On the embedding of BV space into Besov-Orlicz space |
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Institution: | 1. University of Warsaw, Faculty of Mathematics, Informatics and Mechanics, Banacha 2, 02-097 Warsaw, Poland;2. Institute of Mathematics, Polish Academy of Sciences, ?niadeckich 8, 00-656 Warsaw, Poland |
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Abstract: | We give a sufficient (and, in the case of a compact domain, a necessary) condition for the embedding of Sobolev space of functions with integrable gradient into Besov-Orlicz spaces to be bounded. The condition has a form of a simple integral inequality involving Young and weight functions. We provide an example with Matuszewska-Orlicz indices of involved Orlicz norm equal to one. The main tool is the molecular decomposition of functions from a BV space. |
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Keywords: | Besov spaces Orlicz spaces Sobolev spaces |
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