×
Duong, Dao Van; Hong, Ngo Thi

Multilinear Hausdorff operator and commutators on weighted Morrey and Herz spaces. (English) Zbl 1490.42025

Oper. Matrices 15, No. 4, 1541-1557 (2021).
Summary: In this paper, we establish some necessary and sufficient conditions for the boundedness of multilinear Hausdorff operators on weighted central Morrey and Herz type spaces. Moreover, we also discuss some sufficient conditions for the boundedness of commutators of multilinear Hausdorff operators on weighted Morrey-Herz spaces. By these, we generalize some previous known results.

Cited in 1 Document

MSC:

42B35 Function spaces arising in harmonic analysis
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
47B38 Linear operators on function spaces (general)

Keywords:

multilinear operator; Hausdorff operator; Hardy operator; Morrey spaces; Herz spaces; commutators
Cite Review PDF
Full Text: DOI

References:

[1] K. F. ANDERSEN,Boundedness of Hausdorff operators on Lp(Rn), H1(Rn), and BMO(Rn), Acta Sci. Math. (Szeged),69(2003), 409-418. · Zbl 1050.47027
[2] R. BANDALIYEV ANDP. G ´ORKA,Hausdorff operator in Lebesgue spaces, Math. Inequal. Appl.22(2) (2019), 657-676. · Zbl 1462.46029
[3] R. BANDALIYEV ANDK. SAFAROVA,On boundedness of multidimensional Hausdorff operator in weighted Lebesgue spaces, Tbilisi Math. J.13(2020), 39-45. · Zbl 1437.47012
[4] G. BROWN ANDF. M ´ORICZ,Multivariate Hausdorff operators on the spaces Lp(Rn), J. Math. Anal. Appl.271(2002), 443-454. · Zbl 1027.47024
[5] V. I. BURENKOV ANDE. LIFLYAND,Hausdorff operators on Morrey-type spaces, Kyoto J. Math.60 (2020), 93-106. · Zbl 1437.47013
[6] R. R. COIFMAN, R. ROCHBERG ANDG. WEISS,Factorization theorems for Hardy spaces in several variables, Ann. Math.103(1976), 611-635. · Zbl 0326.32011
[7] N. M. CHUONG,Pseudodifferential operators and wavelets over real and p-adicfields, Springer-Basel (2018). · Zbl 1454.35006
[8] N. M. CHUONG, D. V. DUONG ANDK. H. DUNG,Two-weighted inequalities for Hausdorff operators in Herz-type Hardy spaces, Math. Notes106(2019), 20-37. · Zbl 1429.42023
[9] N. M. CHUONG, D. V. DUONG ANDK. H. DUNG,Multilinear Hausdorff operator on variable exponent Morrey-Herz type spaces, Integral Transforms Spec. Funct.31(2020), 62-86. · Zbl 1427.42025
[10] N. M. CHUONG, D. V. DUONG ANDN. D. DUYET,Weighted Morrey-Herz space estimates for rough Hausdorff operator and its commutators, J. Pseudo-Differ. Oper. Appl.11(2020), 753-787. · Zbl 1440.42066
[11] N. M. CHUONG, D. V. DUONG ANDN. D. DUYET,Two-weighted estimates for multilinear Hausdorff operators on the Morrey-Herz spaces, Adv. Oper. Theory5(4) (2020), 1780-1813. · Zbl 1447.42022
[12] N. M. CHUONG, N. T. HONG ANDH. D. HUNG,Multilinear Hardy-Ces‘aro operator and commutator on the product of Morrey-Herz spaces, Anal. Math.43(2017), 547-565. · Zbl 1399.47125
[13] N. M. CHUONG, D. V. DUONG ANDH. D. HUNG,Bounds for the weighted Hardy-Ces‘aro operator and its commutator on Morrey-Herz type spaces, Z. Anal. Anwend.35(2016), 489-504. · Zbl 1448.47060
[14] C. CARTON-LEBRUN ANDM. FOSSET,Moyennes et quotients de Taylor dans BMO, Bull. Soc. Roy. Sci. Li´ege53(1984), 85-87. · Zbl 0543.42013
[15] D. V. DUONG, K. H. DUNG ANDN. M. CHUONG,Weighted estimates for commutators of multilinear Hausdorff operators on variable exponent Morrey-Herz type spaces, Czechoslovak Math. J.70(2020), 833-865. · Zbl 1513.42092
[16] D. V. DUONG,Hausdorff operator and commutator on weighted Morrey-Herz spaces on p -adic fields, Anal. Math. Physics11:31 (2021). · Zbl 1520.47076
[17] J. CHEN, D. FAN ANDJ. LI,Hausdorff operators on function space, Chin. Ann. Math, Series B33 (2012), 537-556. · Zbl 1261.42036
[18] R. R. GOLDBERG,Convolutions and general transforms on Lp, Duke Math. J.27(1960), 251-259. · Zbl 0188.18202
[19] C. GEORGAKIS,The Hausdorff mean of a Fourier-Stieltjes transform, Proc. Amer. Math. Soc.116 (1992), 465-471. · Zbl 0755.42005
[20] G. H. HARDY,Divergent Series, Oxford University Press, Oxford (1949). · Zbl 0032.05801
[21] F. HAUSDORFF,Summation methoden und Momentfolgen, I, Math. Z.9(1921), 74-109. · JFM 48.2005.01
[22] W. A. HURWITZ ANDL. L. SILVERMAN,The consistency and equivalence of certain definitions of summabilities, Trans. Amer. Math. Soc.18(1917), 1-20. · JFM 46.0321.03
[23] H. D. HUNG ANDL. D. KY,New weighted multilinear operators and commutators of Hardy-Ces‘aro type, Acta Math. Sci. Ser. B Engl. Ed.35(2015), 1411-1425. · Zbl 1349.42050
[24] Y. KANJIN,The Hausdorff operators on the real Hardy spaces Hp(R), Studia Math.148(2001), 37-45. · Zbl 1001.47018
[25] E. LIFLYAND ANDF. M ´ORICZ,The Hausdorff operator is bounded on the real Hardy space H1(R), Proc. Amer. Math. Soc.128(2000), 1391-1396. · Zbl 0951.47038
[26] E. LIFLYAND,Hausdorff operators on Hardy spaces, Eurasian Math. J.4(2013), 101-141. · Zbl 1328.47039
[27] E. LIFLYAND ANDA. MIYACHI,Boundedness of the Hausdorff operators in Hpspaces,0<p<1 , Studia Math.194(2009), 279-292. · Zbl 1184.42002
[28] E. LIFLYAND ANDA. MIYACHI,Boundedness of multidimensional Hausdorff operators in Hp spaces,0<p<1 , Trans. Amer. Math. Soc.371(2019), 4793-4814. · Zbl 1440.42097
[29] A. LERNER ANDE. LIFLYAND,Multidimensional Hausdorff operators on real Hardy spaces, J. Austr. Math. Soc.83(2007), 79-86. · Zbl 1143.47023
[30] S. Z. LU, D. C. YANG ANDG. E. HU,Herz type spaces and their applications, Beijing Sci. Press, Beijing (2008).
[31] J. RUAN ANDD. FAN,Hausdorff operators on the power weighted Hardy spaces, J. Math. Anal. Appl.433(2016), 31-48. · Zbl 1331.42018
[32] S. S. VOLOSIVETS,Hausdorff operators on p-adic linear spaces and their properties in Hardy, BMO, and H¨older spaces, Math. Notes3(2013), 382-391. · Zbl 1270.42020
[33] C. TANG, F. XUE ANDY. ZHOU,Commutators of weighted Hardy operators on Herz-type spaces, Ann. Polon. Math.101(3) (2011), 267-273. · Zbl 1230.42023
[34] J. XIAO,Lpand BMO bounds of weighted Hardy-Littlewood averages, J. Math. Anal. Appl.262 (2001), 660-666 · Zbl 1009.42013
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.