Entropy numbers of embeddings of function spaces with Muckenhoupt weights,III. Some limiting cases

We study compact embeddings for weighted spaces of besov and triebel-lizorkin type where the weight belongs to some muckenhoupt a p class. this extends our previous results [25] to more general weights of logarithmically disturbed polynomial growth,both near some singular point and at infinity. we obtain sharp asymptotic estimates for the entropy numbers of this embedding. essential tools are a discretisation in terms of wavelet bases,as well as a refined study of associated embeddings in sequence spaces and interpolation arguments in endpoint situations. copyright © 2011 hindawi publishing corporation.