On the boundedness of Hausdorff operators on Morrey-type spaces
Eurasian mathematical journal, Tome 8 (2017) no. 2, pp. 97-104.

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

We give conditions ensuring the boundedness of Hausdorff operators on Morrey-type spaces. Sharpness of the obtained results is studied, and classes of the Hausdorff operators are described for which the necessary and sufficient conditions coincide.
@article{EMJ_2017_8_2_a6,
     author = {V. I. Burenkov and E. Liflyand},
     title = {On the boundedness of {Hausdorff} operators on {Morrey-type} spaces},
     journal = {Eurasian mathematical journal},
     pages = {97--104},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2017_8_2_a6/}
}
TY  - JOUR
AU  - V. I. Burenkov
AU  - E. Liflyand
TI  - On the boundedness of Hausdorff operators on Morrey-type spaces
JO  - Eurasian mathematical journal
PY  - 2017
SP  - 97
EP  - 104
VL  - 8
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2017_8_2_a6/
LA  - en
ID  - EMJ_2017_8_2_a6
ER  - 
%0 Journal Article
%A V. I. Burenkov
%A E. Liflyand
%T On the boundedness of Hausdorff operators on Morrey-type spaces
%J Eurasian mathematical journal
%D 2017
%P 97-104
%V 8
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2017_8_2_a6/
%G en
%F EMJ_2017_8_2_a6
V. I. Burenkov; E. Liflyand. On the boundedness of Hausdorff operators on Morrey-type spaces. Eurasian mathematical journal, Tome 8 (2017) no. 2, pp. 97-104. http://geodesic.mathdoc.fr/item/EMJ_2017_8_2_a6/

[1] D. R. Adams, Morrey spaces, Birkhäuser, 2015 | MR | Zbl

[2] K. F. Andersen, “Boundedness of Hausdorff operators on $L^p(\mathbb{R}^n)$, $H^1(\mathbb{R}^n)$, and $BMO(\mathbb{R}^n)$”, Acta Sci. Math. (Szeged), 69 (2003), 409–418 | MR | Zbl

[3] G. Brown, F. Móricz, “Multivariate Hausdorff operators on the spaces $L^p(\mathcal{R}^n)$”, J. Math. Anal. Appl., 271 (2002), 443–454 | DOI | MR | Zbl

[4] V. I. Burenkov, “Recent progress in the problem of the boundedness of classical operators of real analysis in general Morrey-type spaces. I”, Eurasian Math. J., 3:3 (2012), 11–32 | MR | Zbl

[5] V. I. Burenkov, “Recent progress in the problem of the boundedness of classical operators of real analysis in general Morrey-type spaces. II”, Eurasian Math. J., 4:1 (2013), 21–45 | MR | Zbl

[6] J. Chen, D. Fan, S. Wang, “Hausdorff operators on Euclidean spaces”, Appl. Math. J. Chinese Univ. (Ser. B) (4), 28 (2014), 548–564 | DOI | MR

[7] C. Georgakis, “The Hausdorff mean of a Fourier–Stieltjes transform”, Proc. Am. Math. Soc., 116 (1992), 465–471 | DOI | MR | Zbl

[8] A. Hussain, G. Gao, “Multidimensional Hausdorff operators and commutators on Herz-type spaces”, J. Inequal. Appl., 594 (2013), 1–12 | DOI | MR

[9] Y. Kanjin, “The Hausdorff operators on the real Hardy spaces $H^p(\mathbb{R})$”, Studia Math., 148 (2001), 37–45 | DOI | MR | Zbl

[10] J. C. Kuang, “Generalized Hausdorff operators on weighted Morrey–Herz spaces”, Acta Math. Sinica (Chin. Ser.), 55 (2012), 895–902, Chinese, English summaries (Chinese) | MR | Zbl

[11] A. Lerner, E. Liflyand, “Multidimensional Hausdorff operator on the real Hardy space”, J. Austr. Math. Soc., 83 (2007), 79–86 | DOI | MR | Zbl

[12] E. Liflyand, “Boundedness of multidimensional Hausdorff operators on $H^1(\mathbb{R}^n)$”, Acta Sci. Math. (Szeged), 74 (2008), 845–851 | MR | Zbl

[13] E. Liflyand, “Hausdorff operators on Hardy spaces”, Eurasian Math. J., 4:4 (2013), 101–141 | MR | Zbl

[14] E. Liflyand, F. Móricz, “The Hausdorff operator is bounded on the real Hardy space $H^1(\mathbb{R}^n)$”, Proc. Am. Math. Soc., 128 (2000), 1391–1396 | DOI | MR | Zbl

[15] F. Móricz, “Multivariate Hausdorff operators on the spaces $H^1(\mathbb{R}^n)$ and $BMO(\mathbb{R}^n)$”, Analysis Math., 31 (2005), 31–41 | DOI | MR | Zbl

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

[17] J. Ruan, D. Fan, “Hausdorff operators on the power weighted Hardy spaces”, J. Math. Anal. Appl., 433 (2016), 31–48 | DOI | MR | Zbl