Geodesic
An analogue of the Littlewood--Paley theorem for orthoprojectors onto wavelet subspaces
Izvestiya. Mathematics , Tome 80 (2016) no. 3, pp. 557-601.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove an analogue of the Littlewood–Paley theorem for orthoprojectors onto wavelet subspaces corresponding to a non-isotropic multiresolution analysis generated by the tensor product of smooth scaling functions of one variable with sufficiently rapid decay at infinity.
Keywords: orthoprojector, wavelet subspaces, scaling function, multiresolution analysis, Littlewood–Paley theorem. 
@article{IM2_2016_80_3_a6,
     author = {S. N. Kudryavtsev},
     title = {An analogue of the {Littlewood--Paley} theorem for orthoprojectors onto wavelet subspaces},
     journal = {Izvestiya. Mathematics },
     pages = {557--601},
     publisher = {mathdoc},
     volume = {80},
     number = {3},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2016_80_3_a6/}
}
TY  - JOUR
AU  - S. N. Kudryavtsev
TI  - An analogue of the Littlewood--Paley theorem for orthoprojectors onto wavelet subspaces
JO  - Izvestiya. Mathematics 
PY  - 2016
SP  - 557
EP  - 601
VL  - 80
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_2016_80_3_a6/
LA  - en
ID  - IM2_2016_80_3_a6
ER  - 
%0 Journal Article
%A S. N. Kudryavtsev
%T An analogue of the Littlewood--Paley theorem for orthoprojectors onto wavelet subspaces
%J Izvestiya. Mathematics 
%D 2016
%P 557-601
%V 80
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_2016_80_3_a6/
%G en
%F IM2_2016_80_3_a6
S. N. Kudryavtsev. An analogue of the Littlewood--Paley theorem for orthoprojectors onto wavelet subspaces. Izvestiya. Mathematics , Tome 80 (2016) no. 3, pp. 557-601. http://geodesic.mathdoc.fr/item/IM2_2016_80_3_a6/

[1] V. N. Temlyakov, “Approximation of functions with a bounded mixed derivative”, Proc. Steklov Inst. Math., 178 (1989), 1–121 | MR | Zbl

[2] È. M. Galeev, “Widths of the Besov classes $B_{p,\theta}^r(\mathbb T^d)$”, Math. Notes, 69:5 (2001), 605–613 | DOI | DOI | MR | Zbl

[3] S. M. Nikol'skii, Approximation of functions of several variables and imbedding theorems, Grundlehren Math. Wiss., 205, Springer-Verlag, New York–Heidelberg, 1975, viii+418 pp. | MR | MR | Zbl | Zbl

[4] O. V. Besov, “The Littlewood–Paley theorem for a mixed norm”, Proc. Steklov Inst. Math., 170 (1987), 33–38 | MR | Zbl

[5] M. Frazier, B. Jawerth, G. Weiss, Littlewood–Paley theory and the study of function spaces, CBMS Reg. Conf. Ser. Math., 79, Amer. Math. Soc., Providence, RI, 1991, viii+132 pp. | DOI | MR | Zbl

[6] N. N. Osipov, “One-sided Littlewood–Paley inequality in $\mathbb R^n$ for $0

\le2$”, J. Math. Sci. (N. Y.), 172:2 (2011), 229–242 | DOI | MR | Zbl

[7] B. Li, M. Bownik, D. Yang, “Littlewood–Paley characterization and duality of weighted anisotropic product Hardy spaces”, J. Funct. Anal., 266:5 (2014), 2611–2661 | DOI | MR | Zbl

[8] S. N. Kudryavtsev, “A Littlewood–Paley type theorem and a corollary”, Izv. Math., 77:6 (2013), 1155–1194 | DOI | DOI | MR | Zbl

[9] Ch. K. Chui, An introduction to wavelets, Wavelet analysis and its applications, 1, Academic Press, Inc., Boston, MA, 1992, x+264 pp. | MR | Zbl

[10] I. Ya. Novikov, V. Yu. Protasov, M. A. Skopina, Wavelet theory, Transl. Math. Monogr., 239, Amer. Math. Soc., Providence, RI, 2011, xiii+506 pp. | MR | MR | Zbl | Zbl

[11] Y. Meyer, Wavelets and operators, Cambridge Stud. Adv. Math., 37, Cambridge Univ. Press, Cambridge, 1992, xvi+224 pp. | MR | Zbl

[12] E. Hernández, G. Weiss, A first course of wavalets, Stud. Adv. Math., CRC Press, Boca Raton, FL, 1996, xx+489 pp. | DOI | MR | Zbl

[13] S. N. Kudryavtsev, Analog teoremy Littlvuda–Peli dlya ortoproektorov na podprostranstva vspleskov, arXiv: 1504.00348

[14] S. N. Kudryavtsev, Teorema tipa Littlvuda–Peli dlya ortoproektorov na podprostranstva vspleskov, arXiv: 1204.1830

[15] S. N. Kudryavtsev, “Obobschennye ryady Khaara i ikh primenenie”, Anal. Math., 37:2 (2011), 103–150 | DOI | MR | Zbl

[16] S. N. Kudryavtsev, “Approximation of the derivatives of finitely smooth functions belonging to non-isotropic classes”, Izv. Math., 68:1 (2004), 77–123 | DOI | DOI | MR | Zbl

[17] S. N. Kudryavtsev, “Approximation and reconstruction of the derivatives of functions satisfying mixed Hölder conditions”, Izv. Math., 71:5 (2007), 895–938 | DOI | DOI | MR | Zbl

[18] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Math. Ser., 30, Princeton Univ. Press, Princeton, NJ, 1970, xiv+290 pp. | MR | MR | Zbl | Zbl

[19] P. Wojtaszczyk, “Wavelets as unconditional bases in $L_p(\mathbb R)$”, J. Fourier Anal. Appl., 5:1 (1999), 73–85 | DOI | MR | Zbl

[20] B. S. Kashin, A. A. Saakyan, Orthogonal series, Transl. Math. Monogr., 75, Amer. Math. Soc., Providence, RI, 1989, xii+451 pp. | MR | MR | Zbl | Zbl