Banach Journal of Mathematical Analysis

The isomorphic classification of Besov spaces over Rd revisited

Fernando Albiac and José Luis Ansorena

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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

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

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

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Zentralblatt MATH identifier

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]

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


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.

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