Abstract
In this paper, we study the spaces B s pq (G) and L s pq (G) of functions with positive exponent of smoothness s > 0, defined on a domain \(\user1{G} \subset \mathbb{R}^\user1{n} \). For a domain G with specific geometric properties, we establish the embedding B s pq (G) = L s pq (G) ⊂ L q (G), 1 < p < q < ∞, with the relationship between the parameters defined by these geometric properties.
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Besov, O.V. Spaces of Functions of Fractional Smoothness on an Irregular Domain. Mathematical Notes 74, 157–176 (2003). https://doi.org/10.1023/A:1025095906229
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DOI: https://doi.org/10.1023/A:1025095906229