Publication: On the Relationship Between Two Kinds of Besov Spaces with Smoothness Near Zero and Some Other Applications of Limiting Interpolation
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2015
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Birkhauser
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Abstract
Using limiting interpolation techniques we study the elationship between Besov spaces B0,−1/q p,q with zero classical smoothness and logarithmic smoothness −1/q defined by means of differences with similar spaces 0,b,d p,q defined by means of the Fourier transform. Among other things, we prove that B0,−1/2 2,2 = B0,0,1/2 2,2 . We also derive several results on periodic spaces B0,−1/q p,q (T), including embeddings in generalized Lorentz–Zygmund spaces and the distribution of Fourier coefficients of functions of B0,−1/q p,q (T).