Some remarks on the Boyd functions related to the admissible sequences

[en] In this paper, we discuss the existing relations between the Boyd functions and the admissible sequences, with a particular interest to the Boyd indices. We introduce several results binding these notions and propose some constructions to obtain a Boyd function from an admissible sequence. We finally discuss the notion of generalized interpolation space based on these concepts.

Disciplines :

Mathematics

Author, co-author :

Lamby, Thomas ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Nicolay, Samuel ; Université de Liège - ULiège > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes

Language :

English

Title :

Some remarks on the Boyd functions related to the admissible sequences

Publication date :

30 August 2022

Journal title :

Zeitschrift für Analysis und ihre Anwendungen

ISSN :

0232-2064

eISSN :

1661-4534

Publisher :

European Mathematical Society - EMS - Publishing House GmbH

Volume :

Pages :

211-227

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 02 November 2022

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Bibliography

A. Almeida, Wavelet bases in generalized Besov spaces. J. Math. Anal. Appl. 304 (2005), 198–211
J. Bergh and J. Löfström. Interpolation spaces: An introduction. Grundlehren Math. Wiss. 223, Springer, Berlin, 1976
N. H. Bingham, C. M. Goldie and J. L. Teugels, Regular variation. Encyclopedia Math. Appl. 27, Cambridge University Press, Cambridge, 1987
D. W. Boyd, The Hilbert transform on rearrangement-invariant spaces. Canadian J. Math. 19 (1967), 599–616
D. W. Boyd, Indices of function spaces and their relationship to interpolation. Canadian J. Math. 21 (1969), 1245–1254
M. Bricchi, Tailored Besov spaces and h-sets. Math. Nachr. 263/264 (2004), 36–52; PhD thesis, University of Jena, 2002
M. Bricchi and S. D. Moura, Complements on growth envelopes of spaces with generalized smoothness in the sub-critical case. Z. Anal. Anwendungen 22 (2003), 383–398
A. M. Caetano and W. Farkas, Local growth envelopes of Besov spaces of generalized smoothness. Z. Anal. Anwend. 25 (2006), 265–298
F. Cobos and D. L. Fernandez, Hardy–Sobolev spaces and Besov spaces with a function parameter. In Function spaces and applications (Lund, 1986), pp. 158–170, Lecture Notes in Math. 1302, Springer, Berlin, 1988
W. Farkas and H.-G. Leopold, Characterisations of function spaces of generalised smoothness. Ann. Mat. Pura Appl. (4) 185 (2006), 1–62
D. D. Haroske and S. D. Moura, Continuity envelopes and sharp embeddings in spaces of generalized smoothness. J. Funct. Anal. 254 (2008), 1487–1521
W. B. Johnson, B. Maurey, G. Schechtman and L. Tzafriri, Symmetric structures in Banach spaces. Mem. Amer. Math. Soc. 19 (1979), v+298
G. A. Kaljabin, Characterization of spaces with generalized Liouville differentiation. Math. USSR Sb. 33 (1977), 37
D. Kreit and S. Nicolay, Generalized pointwise Hölder spaces defined via admissible sequences. J. Funct. Spaces (2018), Art. ID 8276258, 11
S. G. Kreın, Y. I. Petunin and E. M. Semënov, Interpolation of linear operators. Transl. Math. Monogr. 54, American Mathematical Society, Providence, 1982
T. Kühn, H.-G. Leopold, W. Sickel and L. Skrzypczak, Entropy numbers of embeddings of weighted Besov spaces. II. Proc. Edinb. Math. Soc. (2) 49 (2006), 331–359
L. Loosveldt and S. Nicolay, Some equivalent definitions of Besov spaces of generalized smoothness. Math. Nachr. 292 (2019), 2262–2282
L. Loosveldt and S. Nicolay, Generalized Tup spaces: On the trail of Calderón and Zygmund. Dissertationes Math. 554 (2020), 64
C. Merucci, Applications of interpolation with a function parameter to Lorentz, Sobolev and Besov spaces. In Interpolation spaces and allied topics in analysis (Lund, 1983), pp. 183–201, Lecture Notes in Math. 1070, Springer, Berlin, 1984
S. D. Moura, J. S. Neves and C. Schneider, Spaces of generalized smoothness in the critical case: Optimal embeddings, continuity envelopes and approximation numbers. J. Approx. Theory 187 (2014), 82–117

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