Generalized weighted Morrey spaces and higher order commutators of sublinear operators
Eurasian mathematical journal, Tome 3 (2012) no. 3, pp. 33-61.

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

In this paper, we study the boundedness of sublinear operators and their higher order commutators generated by Calderon–Zygmund operators and Riesz potentials on generalized weighted Morrey space.
@article{EMJ_2012_3_3_a3,
     author = {V. S. Guliyev},
     title = {Generalized weighted {Morrey} spaces and higher order commutators of sublinear operators},
     journal = {Eurasian mathematical journal},
     pages = {33--61},
     publisher = {mathdoc},
     volume = {3},
     number = {3},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2012_3_3_a3/}
}
TY  - JOUR
AU  - V. S. Guliyev
TI  - Generalized weighted Morrey spaces and higher order commutators of sublinear operators
JO  - Eurasian mathematical journal
PY  - 2012
SP  - 33
EP  - 61
VL  - 3
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2012_3_3_a3/
LA  - en
ID  - EMJ_2012_3_3_a3
ER  - 
%0 Journal Article
%A V. S. Guliyev
%T Generalized weighted Morrey spaces and higher order commutators of sublinear operators
%J Eurasian mathematical journal
%D 2012
%P 33-61
%V 3
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2012_3_3_a3/
%G en
%F EMJ_2012_3_3_a3
V. S. Guliyev. Generalized weighted Morrey spaces and higher order commutators of sublinear operators. Eurasian mathematical journal, Tome 3 (2012) no. 3, pp. 33-61. http://geodesic.mathdoc.fr/item/EMJ_2012_3_3_a3/

[1] D. R. Adams, “A note on Riesz potentials”, Duke Math., 42 (1975), 765–778 | DOI | MR | Zbl

[2] A. Akbulut, I. Ekincioglu, A. Serbetci, T. Tararykova, “Boundedness of the anisotropic fractional maximal operator in anisotropic local Morrey-type spaces”, Eurasian Mathematical Journal, 2:2 (2011), 5–30 | MR | Zbl

[3] A. Akbulut, V. S. Guliyev, R. Mustafayev, “On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces”, Mathematica Bohemica, 137:1 (2012), 27–43 | MR | Zbl

[4] V. I. Burenkov, V. S. Guliyev, “Necessary and sufficient conditions for the boundedness of the Riesz potential in local Morrey-type spaces”, Potential Anal., 30:3 (2009), 211–249 | DOI | MR | Zbl

[5] V. I. Burenkov, V. S. Guliyev, A. Serbetci, T. V. Tararykova, “Necessary and sufficient conditions for the boundedness of genuine singular integrals in local Morrey-type spaces”, Eurasian Mathematical Journal, 1:1 (2010), 32–53 | MR | Zbl

[6] S. Chanillo, “A note on commutators”, Indiana Univ. Math. J., 23 (1982), 7–16 | DOI | MR

[7] M. Carro, L. Pick, J. Soria, V. D. Stepanov, “On embeddings between classical Lorentz spaces”, Math. Inequal. Appl., 4:3 (2001), 397–428 | MR | Zbl

[8] F. Chiarenza, M. Frasca, “Morrey spaces and Hardy–Littlewood maximal function”, Rend Mat., 7 (1987), 273–279 | MR | Zbl

[9] R. R. Coifman, C. Fefferman, “Weighted norm inequalities for maximal functions and singular integrals”, Studia Math., 51 (1974), 241–250 | MR | Zbl

[10] A. Gogatishvili, R. Mustafayev, “On a theorem of Muckenhouopt–Wheeden in generalized Morrey spaces”, Eurasian Mathematical Journal, 2:2 (2011), 134–138 | MR | Zbl

[11] R. Coifman, Y. Meyer, Au delà des Opérateurs Pseudo-Différentiels, Astérisque, 57, Société Mathématique de France, Paris, 1978 | MR

[12] Y. Ding, D. Yang, Z. Zhou, “Boundedness of sublinear operators and commutators on $L^{p,\omega}(\mathbb R^n)$”, Yokohama Math. J., 46 (1998), 15–27 | MR | Zbl

[13] X. T. Duong, L. X. Yan, “On commutators of fractional integrals”, Proc. Amer. Math. Soc., 132:12 (2004), 3549–3557 | DOI | MR | Zbl

[14] J. Garcia-Cuerva, J. L. Rubio de Francia, Weighted Norm Inequalities and Related Topics, North-Holland Math., 16, Amsterdam, 1985 | MR

[15] L. Grafakos, Classical and Modern Fourier Analysis, Pearson Education, Inc., Upper Saddle River, New Jersey, 2004 | MR | Zbl

[16] V. S. Guliyev, “Boundedness of the maximal, potential and singular operators in the generalized Morrey spaces”, J. Inequal. Appl., 2009 (2009), Art. ID 503948, 20 pp. | MR

[17] V. S. Guliyev, S. S. Aliyev, T. Karaman, “Boundedness of sublinear operators and commutators on generalized Morrey spaces”, Abstr. Appl. Anal., 2011 (2011), Art. ID 356041, 18 pp. | DOI | MR

[18] V. S. Guliyev, S. S. Aliyev, T. Karaman, P. Shukurov, “Boundedness of sublinear operators and commutators on generalized Morrey spaces”, Integral Equations Operator Theory, 71:3 (2011), 327–355 | DOI | MR | Zbl

[19] V. S. Guliyev, S. S. Aliyev, “Boundedness of parametric Marcinkiewicz integral operator and their commutators on generalized Morrey spaces”, Georgian Math. J., 19 (2012), 195–208 | MR

[20] V. S. Guliyev, T. Karaman, A. Serbetci, “Boundedness of sublinear operators generated by Calderon–Zygmund operators on generalized weighted Morrey spaces”, Scientic Annals of “Al. I. Cuza” University of Iasi, 2011, 18 pp., accepted

[21] V. S. Guliyev, T. Karaman, R. Ch. Mustafayev, A. Serbetci, Commutators of sublinear operators generated by Calderón–Zygmund operator on generalized weighted Morrey spaces, submitted

[22] Y. Komori, S. Shirai, “Weighted Morrey spaces and a singular integral operator”, Math. Nachr., 282:2 (2009), 219–231 | DOI | MR | Zbl

[23] Y. Lin, Sh. Lu, “Strongly singular Calderón–Zygmund operators and their commutators”, Jordan Journal of Mathematics and Statistics, 1:1 (2008), 31–49 | Zbl

[24] L. Z. Liu, “Weighted weak type estimates for commutators of Littlewood–Paley operator”, Japan. J. Math. (N.S.), 29:1 (2003), 1–13 | MR | Zbl

[25] Y. Liu, D. Chen, “The boundedness of maximal Bochner–Riesz operator and maximal commutator on Morrey type spaces”, Anal. Theory Appl., 24:4 (2008), 321–329 | DOI | MR | Zbl

[26] L. Z. Liu, S. Z. Lu, “Weighted weak type inequalities for maximal commutators of Bochner–Riesz operator”, Hokkaido Math. J., 32:1 (2003), 85–99 | DOI | MR | Zbl

[27] G. Lu, S. Lu, D. Yang, “Singular integrals and commutators on homogeneous groups”, Anal. Math., 28 (2002), 103–134 | DOI | MR | Zbl

[28] S. Lu, Y. Ding, D. Yan, Singular integrals and related topics, World Scientific Publishing, Singapore, 2006 | MR

[29] B. Muckenhoupt, “Weighted norm inequalities for the Hardy maximal function”, Trans. Amer. Math. Soc., 165 (1972), 207–226 | DOI | MR | Zbl

[30] B. Muckenhoupt, R. Wheeden, “Weighted norm inequalities for fractional integrals”, Trans. Amer. Math. Soc., 192 (1974), 261–274 | DOI | MR | Zbl

[31] C. B. Morrey, “On the solutions of quasi-linear elliptic partial differential equations”, Trans. Amer. Math. Soc., 43 (1938), 126–166 | DOI | MR | Zbl

[32] J. Peetre, “On the theory of $M_{p,\lambda}$”, J. Funct. Anal., 4 (1969), 71–87 | DOI | MR | Zbl

[33] X. Shi, Q. Sun, “Weighted norm inequalities for Bochner–Riesz operators and singular integral operators”, Proc. Amer. Math. Soc., 116 (1992), 665–673 | DOI | MR | Zbl

[34] F. Soria, G. Weiss, “A remark on singular integrals and power weights”, Indiana Univ. Math. J., 43 (1994), 187–204 | DOI | MR | Zbl

[35] E. M. Stein, Singular integrals and differentiability of functions, Princeton University Press, Princeton, NJ, 1970

[36] E. M. Stein, “On the functions of Littlewood–Paley, Lusin, and Marcinkiewicz”, Trans. Amer. Math. Soc., 88 (1958), 430–466 | DOI | MR

[37] E. M. Stein, Harmonic Analysis: Real Variable Methods, Orthogonality and Oscillatory Integrals, Princeton Univ. Press, Princeton, NJ, 1993 | MR | Zbl

[38] A. Vargas, “Weighted weak type (1,1) bounds for rough operators”, J. Lond. Math. Soc., 54:2 (1996), 297–310 | DOI | MR | Zbl

[39] A. Torchinsky, Real Variable Methods in Harmonic Analysis, Pure and Applied Math., 123, Academic Press, New York, 1986 | MR | Zbl

[40] A. Torchinsky, S. Wang, “A note on the Marcinkiewicz integral”, Colloq. Math., 60/61 (1990), 235–243 | MR | Zbl