“…Rychkov extended in [31] the above class of weights in order to incorporate locally regular weights, too, creating in that way the class A loc p . Recent works are due to Roudenko [29,30,13], and Bownik [1,2].…”
Abstract. We study compact embeddings for weighted spaces of Besov and Triebel-Lizorkin type where the weights belong to Muckenhoupt A p classes. We focus our attention on the influence of singular points of the weights on the compactness of the embeddings as well as on the asymptotic behaviour of their entropy and approximation numbers.
“…Rychkov extended in [31] the above class of weights in order to incorporate locally regular weights, too, creating in that way the class A loc p . Recent works are due to Roudenko [29,30,13], and Bownik [1,2].…”
Abstract. We study compact embeddings for weighted spaces of Besov and Triebel-Lizorkin type where the weights belong to Muckenhoupt A p classes. We focus our attention on the influence of singular points of the weights on the compactness of the embeddings as well as on the asymptotic behaviour of their entropy and approximation numbers.
“…In all these references the definitions are Fourier analytic. For the class W 1 these different approaches coincide (see [10,29,[35][36][37][38]). Remark 2.6.…”
We investigate the asymptotic behaviour of the entropy numbers of the compact embed-denotes a weighted Besov space. We present a general approach which allows us to work with a large class of weights.
“…In case of Muckenhoupt weights we refer to [22]. The combination of Muckenhoupt weights and weights which even may grow exponentially has been given in [25].…”
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