A localization property for $B^{s}_{pq}$ and $F^{s}_{pq}$ spaces

Triebel, Hans

A localization property for

B_{p q}^{s}

and

F_{p q}^{s}

spaces

Triebel, Hans

Studia Mathematica, Tome 108 (1994), p. 183-195 / Harvested from The Polish Digital Mathematics Library

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Résumé

Let $f^{j} = \sum_{k} a_{k} f (2^{j + 1} x - 2 k)$ , where the sum is taken over the lattice of all points k in $ℝ^{n}$ having integer-valued components, j∈ℕ and $a_{k} \in ℂ$ . Let $A_{p q}^{s}$ be either $B_{p q}^{s}$ or $F_{p q}^{s}$ (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on $ℝ^{n} .$ The aim of the paper is to clarify under what conditions $∥ f^{j} | A_{p q}^{s} ∥$ is equivalent to $2^{j (s - n / p)} (\sum_{k} | a_{k} |^{p})^{1 / p} ∥ f | A_{p q}^{s} ∥$ .

Publié le : 1994-01-01

Zbl 0819.46025

EUDML-ID : urn:eudml:doc:216068

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     author = {Hans Triebel},
     title = {A localization property for $B^{s}\_{pq}$ and $F^{s}\_{pq}$ spaces},
     journal = {Studia Mathematica},
     volume = {108},
     year = {1994},
     pages = {183-195},
     zbl = {0819.46025},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv109i2p183bwm}
}

Triebel, Hans. A localization property for $B^{s}_{pq}$ and $F^{s}_{pq}$ spaces. Studia Mathematica, Tome 108 (1994) pp. 183-195. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv109i2p183bwm/

Bibliographie

[00000] [1] I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Regional Conf. Ser. in Appl. Math. 61, SIAM, Philadelphia, 1992.

[00001] [2] D. E. Edmunds and H. Triebel, Eigenvalue distributions of some degenerate elliptic operators: an approach via entropy numbers, Math. Ann., to appear. | Zbl 0804.35097

[00002] [3] M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), 777-799. | Zbl 0551.46018

[00003] [4] M. Frazier and B. Jawerth, A discrete transform and decomposition of distribution spaces, J. Funct. Anal. 93 (1990), 34-170.

[00004] [5] M. Frazier, B. Jawerth and G. Weiss, Littlewood-Paley Theory and the Study of Function Spaces, CBMS Regional Conf. Ser. in Math. 79, Amer. Math. Soc., Providence, 1991. | Zbl 0757.42006

[00005] [6] W. Sickel and H. Triebel, Hölder inequalities and sharp embeddings in function spaces of $B_{p} q^{s}$ and $F_{p} q^{s}$ type, submitted.

[00006] [7] R. H. Torres, Boundedness results for operators with singular kernels on distribution spaces, Mem. Amer. Math. Soc. 442 (1991). | Zbl 0737.47041

[00007] [8] H. Triebel, Theory of Function Spaces, Birkhäuser, Basel, 1983.

[00008] [9] H. Triebel, Theory of Function Spaces, II, Birkhäuser, Basel, 1992.

[00009] [10] H. Triebel, Approximation numbers and entropy numbers of embeddings of fractional Besov-Sobolev spaces in Orlicz spaces, Proc. London Math. Soc. 66 (1993), 589-618. | Zbl 0792.46024