Geodesic
Modified Hardy and Hardy--Littlewood fractional operators in Morrey--Herz spaces and their commutators in weighted spaces
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 70-77.

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

In this paper, we obtain sufficient conditions of the boundedness of modified fractional Hardy–Littlewood and Hardy operators from one modified Morrey–Herz space to another. We also study the boundedness of commutators of these operators from one weighted space with a power weight to another.
Keywords: Hardy–Littlewood fractional operator, Hardy fractional operator, modified Morrey–Herz space, weighted space $L^q$, commutator. 
@article{INTO_2019_171_a5,
     author = {S. S. Volosivets and B. I. Golubov},
     title = {Modified {Hardy} and {Hardy--Littlewood} fractional operators in {Morrey--Herz} spaces and their commutators in weighted spaces},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {70--77},
     publisher = {mathdoc},
     volume = {171},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_171_a5/}
}
TY  - JOUR
AU  - S. S. Volosivets
AU  - B. I. Golubov
TI  - Modified Hardy and Hardy--Littlewood fractional operators in Morrey--Herz spaces and their commutators in weighted spaces
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2019
SP  - 70
EP  - 77
VL  - 171
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2019_171_a5/
LA  - ru
ID  - INTO_2019_171_a5
ER  - 
%0 Journal Article
%A S. S. Volosivets
%A B. I. Golubov
%T Modified Hardy and Hardy--Littlewood fractional operators in Morrey--Herz spaces and their commutators in weighted spaces
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2019
%P 70-77
%V 171
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2019_171_a5/
%G ru
%F INTO_2019_171_a5
S. S. Volosivets; B. I. Golubov. Modified Hardy and Hardy--Littlewood fractional operators in Morrey--Herz spaces and their commutators in weighted spaces. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh Winter Mathematical School "Modern Methods of Function Theory and Related Problems." January 28 – February 2, 2019. Part 2, Tome 171 (2019), pp. 70-77. http://geodesic.mathdoc.fr/item/INTO_2019_171_a5/

[1] Volosivets S. S., “Modifitsirovannye operatory Khardi i Khardi—Littlvuda i ikh povedenie v razlichnykh prostranstvakh”, Izv. RAN. Ser. mat., 75:1 (2011), 29–52 | DOI | MR | Zbl

[2] Golubov B. I., Efimov A. V., Skvortsov V. A., Ryady i preobrazovaniya Uolsha, Nauka, M., 1987 | MR

[3] Golubov B. I., “O dvoichnykh analogakh operatorov Khardi i Khardi—Littlvuda”, Sib. mat. zh., 40:6 (1999), 1244–1252 | MR

[4] Golubov B. I., “Ob ogranichennosti dvoichnykh operatorov Khardi i Khardi—Littlvuda v dvoichnykh prostranstvakh $H$ i $BMO$”, Anal. Math., 26:4 (2000), 287–298 | DOI | MR | Zbl

[5] Khardi G. G., Littlvud Dzh. E., Polia G., Neravenstva, IL, M., 1948

[6] Adams D. R., Morrey Spaces, Birkhäuser, Basel, 2015 | MR | Zbl

[7] Andersen K. F., Muckenhoupt B., “Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions”, Stud. Math., 72:1 (1982), 9–26 | DOI | MR | Zbl

[8] Drabek P., Heinig H., Kufner A., “Higher-dimensional Hardy inequality”, General Inequalities, eds. Bandle C., Everitt W. N., et al., Springer, Basel, 1997, 3–16 | DOI | MR

[9] Gao G., Zhong Y., “Some estimates of Hardy operators and their commutators on Morrey–Herz spaces”, J. Math. Ineq., 11:1 (2017), 49–58 | DOI | MR | Zbl

[10] Herz C., “Lipschitz spaces and Bernstein's theorem on absolutely convergent Fourier transforms”, J. Math. Mech., 18:4 (1968), 283–324 | MR

[11] Onneweer C. W., “Generalized Lipschitz spaces and Herz spaces on certain totally disconnected groups”, Martingale Theory in Harmonic Analysis and Banach Spaces, Lect. Notes Math., 939, Springer-Verlag, Berlin, 1981, 106–121 | DOI | MR

[12] Volosivets S. S., “On $P$-adic analogs of Hardy and Hardy-Littlewood operators”, East J. Approx., 11:1 (2005), 57–72 | MR | Zbl