Banach Journal of Mathematical Analysis

The isomorphic classification of Besov spaces over Rd revisited

Fernando Albiac and José Luis Ansorena

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Abstract

We take advantage of the recent developments in the isomorphic classification of the infinite matrix spaces of mixed norms q(p) for the whole range of values 0<p,q to give a unified approach to the classification of Besov spaces over Euclidean spaces. In particular, we show that different Besov spaces with generalized smoothness B ˚ p,qw(Rd) over the Euclidean space Rd are isomorphic if and only if the indices p and q match.

Article information

Source
Banach J. Math. Anal., Volume 10, Number 1 (2016), 108-119.

Dates
Received: 6 March 2015
Accepted: 17 April 2015
First available in Project Euclid: 11 November 2015

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1447253823

Digital Object Identifier
doi:10.1215/17358787-3336542

Mathematical Reviews number (MathSciNet)
MR3453526

Zentralblatt MATH identifier
1354.46034

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems
Secondary: 42B35: Function spaces arising in harmonic analysis 46B25: Classical Banach spaces in the general theory 46B03: Isomorphic theory (including renorming) of Banach spaces 46B45: Banach sequence spaces [See also 46A45]

Keywords
Besov spaces (weighted) $L_{p}$-spaces wavelets sequence spaces isomorphic classification

Citation

Albiac, Fernando; Ansorena, José Luis. The isomorphic classification of Besov spaces over $\mathbb{R}^{d}$ revisited. Banach J. Math. Anal. 10 (2016), no. 1, 108--119. doi:10.1215/17358787-3336542. https://projecteuclid.org/euclid.bjma/1447253823


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References

  • [1] F. Albaic and J. L. Ansorena, On the mutually non isomorphic $\ell_{p}(\ell_{q})$ spaces, II, Math. Nachr. 288 (2015), no. 1, 5–9.
  • [2] F. Albiac and N. J. Kalton, Topics in Banach Space Theory, Grad. Texts in Math. 233, Springer, New York, 2006.
  • [3] A. Almeida, Wavelet bases in generalized Besov spaces, J. Math. Anal. Appl. 304 (2005), no. 1, 198–211.
  • [4] J. L. Ansorena and O. Blasco, Characterization of weighted Besov spaces, Math. Nachr. 171 (1995), 5–17.
  • [5] J. L. Ansorena and O. Blasco, Convolution multipliers on weighted Besov spaces, Bol. Soc. Mat. Mexicana (3) 4 (1998), no. 1, 47–68.
  • [6] P. Cembranos and J. Mendoza, On the mutually non isomorphic $\ell_{p}(\ell_{q})$ spaces, Math. Nachr. 284 (2011), no. 16, 2013–2023.
  • [7] W. Farkas and H. Leopold, Characterisations of function spaces of generalised smoothness, Ann. Mat. Pura Appl. (4) 185 (2006), no. 1, 1–62.
  • [8] M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), no. 4, 777–799.
  • [9] M. Frazier and B. Jawerth, “Applications of the $\phi$ and wavelet transforms to the theory of function spaces” in Wavelets and Their Applications, Jones and Bartlett, Boston, 1992, 377–417.
  • [10] M. Frazier, B. Jawerth, and G. Weiss, Littlewood-Paley Theory and the Study of Function Spaces, CBMS Regional Conference Series in Mathematics 79, Amer. Math. Soc., Providence, 1991.
  • [11] P. G. Lemarié and Y. Meyer, Ondelettes et bases hilbertiennes, Rev. Mat. Iberoamericana 2 (1986), no. 1–2, 1–18.
  • [12] J. Peetre, New Thoughts on Besov Spaces, Duke Univ. Math. Ser. 1, Department of Mathematics, Duke University, Durham, NC, 1976.
  • [13] A. Pietsch, History of Banach Spaces and Linear Operators, Birkhäuser, Boston, 2007.
  • [14] W. Rudin, Functional Analysis, 2nd ed., Internat. Ser. Pure Appl. Math., McGraw-Hill, New York, 1991.
  • [15] H. Triebel, Über die Existenz von Schauderbasen in Sobolev-Besov-Räumen: Isomorphiebeziehungen, Studia Math. 46 (1973), 83–100 (German).
  • [16] H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978.