Publication: Duality for logarithmic interpolation spaces and applications to Besov spaces
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We review several results on duality of logarithmic interpolation spaces and applications to Besov spaces. We also establish some new results on Besov spaces with smoothness close to zero defined by differences.
 C. Bennett and R. Sharpley, Interpolation of Operators, Academic Press, Boston, 1988.  J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer, Berlin, 1976.  B.F. Besoy and F. Cobos, Duality for logarithmic interpolation spaces when 0 < q < 1 applications, J. Math. Anal. Appl. 466 (2018) 373–399.  Yu. A. Brudny˘ı and N. Ya. Krugljak, Interpolation Functors and Interpolation Spaces, Vol. 1, North-Holland, Amsterdam, 1991.  A.M. Caetano, A. Gogatishvili and B. Opic, Sharp embeddings of Besov spaces involving only logarithmic smoothness, J. Approx. Theory 152 (2008) 188–214.  F. Cobos, Duality and Lorentz-Marcinkiewicz operator spaces, Math. Scand. 63 (1988) 261–267.  F. Cobos and O. Domínguez, Approximation spaces, limiting interpolation and Besov spaces, J. Approx. Theory 189 (2015) 43–66.  F. Cobos and O. Domínguez, On Besov spaces of logarithmic smoothness and Lipschitz spaces, J. Math. Anal. Appl. 425 (2015) 71–84.  F. Cobos and O. Domínguez, On the relationship between two kinds of Besov spaces with smoothness near zero and some other applications of limiting interpolation, J. Fourier Anal. Appl. 22 (2016) 1174–1191.  F. Cobos, O. Domínguez and T. Kühn, Approximation and entropy numbers of embed- dings between approximation spaces, Constr. Approx. 47 (2018) 453–486.  F. Cobos, O. Domínguez and H. Triebel, characterizations of logarithmic Besov spaces in terms of differences, Fourier-analytical decompositions, wavelets and semi-groups, J. Funct. Anal. 270 (2016) 4386–4425.  F. Cobos and D.L. Fernandez, Hardy-Sobolev spaces and Besov spaces with a function parameter in Function Spaces and Applications, in Lecture Notes in Math., vol. 1302, Springer, Berlin, 1988, pp. 158–170.  F. Cobos, L. M. Fernández-Cabrera, T. Kühn and T. Ullrich, On an extreme class of real interpolation spaces, J. Funct. Anal. 256 (2009) 2321–2366.  F. Cobos, L. M. Fernández-Cabrera and M. Mastyło, Abstract limit J -spaces, J. London Math. Soc. 82 (2010) 501–525.  F. Cobos and T. Kühn, Approximation and entropy numbers in Besov spaces of gener- alized smoothness, J. Approx. Theory 160 (2009) 56–70.  F. Cobos and T. Kühn, Equivalence of K and J -methods for limiting real interpolation spaces, J. Funct. Anal. 261 (2011) 3696–3722.  F. Cobos and A. Segurado, Description of logarithmic interpolation spaces by means of the J -functional and applications, J. Funct. Anal. 286 (2015) 2906–2945.  M. Cwikel and J. Peetre, Abstract K and J spaces, J. Math. Pures Appl. 60 (1981) 1–50.  W.D. Evans and B. Opic, Real interpolation with logarithmic functors and reiteration, Canad. J. Math. 52 (2000) 920–960.  W.D. Evans, B. Opic and L. Pick, Real interpolation with logarithmic functors, J. Inequal. Appl. 7 (2002) 187–269.  F. Fehér and G. Grässler, On an extremal scale of approximation spaces, J. Comput. Anal. Appll. 3 (2001) 95–108.  J. Gustavsson, A function parameter in connection with interpolation of Banach spaces, Math. Scand. 42 (1978) 289–305.  D.D. Haroske, On more general Lipschitz spaces, Z. Anal. Anwend 19 (2000) 781–799.  D.D. Haroske, Envelopes and Sharp Embeddings of Function Spaces, Chapman & Hall/CRC Res. Notes Math., vol. 437, Chapman & Hall/CRC, Boca Raton, FL, 2007.  D.D. Haroske and S.D. Moura, Continuity envelopes of spaces of generalized smoothness, entropy and approximation numbers, J. Approx. Theory 128 (2004) 151–174.  S. Janson, Minimal and maximal methods of interpolation, J. Funct. Anal. 44 (1981) 50–73.