António M. Caetano

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Continuity envelopes for the spaces of generalised smoothness B (s,Ψ) pq (R n) and F (s,Ψ) pq (R n) are studied in the so-called supercritical case s = 1 + n/p, paralleling recent developments for a corresponding limiting case for local growth envelopes of spaces of such a type. In addition, the power of the concept is used in proving conditions for some(More)
We characterize local embeddings of Besov spaces B 0,b p,r involving only a slowly varying smoothness b into classical Lorentz spaces. These results are applied to establish sharp local embeddings of Besov spaces in question into Lorentz-Karamata spaces. As consequence of these results, we are able to determine growth envelopes of spaces B 0,b p,r and to(More)
We use Kolyada's inequality and its converse form to prove sharp embeddings of Besov spaces B 0,β p,r (involving the zero classical smoothness and a logarithmic smoothness with the exponent β) into Lorentz-Zygmund spaces. We also determine growth envelopes of spaces B 0,β p,r. In distinction to the case when the classical smoothness is positive, we show(More)
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