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      Weak boundedness for the commutator of $n$-dimensional rough Hardy operator on homogeneous Herz spaces and central Morrey spaces

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      https://www.riss.kr/link?id=A109165199

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      다국어 초록 (Multilingual Abstract) kakao i 다국어 번역

      In this paper, we study the boundedness of the commutator $H_\Omega^b$ formed by the rough Hardy operator $H_\Omega$ and a locally integrable function $b$ from homogeneous Herz spaces to homogeneous weak Herz spaces. In addition, the weak boundedness of $H_\Omega^b$ on central Morrey spaces is also established.
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      In this paper, we study the boundedness of the commutator $H_\Omega^b$ formed by the rough Hardy operator $H_\Omega$ and a locally integrable function $b$ from homogeneous Herz spaces to homogeneous weak Herz spaces. In addition, the weak boundedness ...

      In this paper, we study the boundedness of the commutator $H_\Omega^b$ formed by the rough Hardy operator $H_\Omega$ and a locally integrable function $b$ from homogeneous Herz spaces to homogeneous weak Herz spaces. In addition, the weak boundedness of $H_\Omega^b$ on central Morrey spaces is also established.

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      참고문헌 (Reference)

      1 K. Andersen, "Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions" 72 (72): 9-26, 1982

      2 Q. Y. Wu, "Weighted p-adic Hardy operators and their commutators on p-adic central Morrey spaces" 40 (40): 635-654, 2017

      3 Z. Fu, "Weighted multilinear Hardy operators and commutators" 27 (27): 2825-2851, 2015

      4 J. Ruan, "Weighted Morrey estimates for Hausdorff operator and its commutator on the Heisenberg group" 22 (22): 307-329, 2019

      5 E. Sawyer, "Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator" 281 (281): 329-337, 1984

      6 W. G. Faris, "Weak Lebesgue spaces and quantum mechanical binding" 43 (43): 365-373, 1976

      7 Z. Fu, "Two characterizations of central BMO space via the commutators of Hardy operators" 33 (33): 505-529, 2021

      8 S. Lu, "The weighted Herz-type Hardy space and its applications" 38 (38): 662-673, 1995

      9 W. Guo, "The unified theory for the necessity of bounded commutators and applications" 30 (30): 3995-4035, 2020

      10 S. Lu, "The central BMO spaces and Littlewood–Paley operators" 11 (11): 72-94, 1995

      1 K. Andersen, "Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions" 72 (72): 9-26, 1982

      2 Q. Y. Wu, "Weighted p-adic Hardy operators and their commutators on p-adic central Morrey spaces" 40 (40): 635-654, 2017

      3 Z. Fu, "Weighted multilinear Hardy operators and commutators" 27 (27): 2825-2851, 2015

      4 J. Ruan, "Weighted Morrey estimates for Hausdorff operator and its commutator on the Heisenberg group" 22 (22): 307-329, 2019

      5 E. Sawyer, "Weighted Lebesgue and Lorentz norm inequalities for the Hardy operator" 281 (281): 329-337, 1984

      6 W. G. Faris, "Weak Lebesgue spaces and quantum mechanical binding" 43 (43): 365-373, 1976

      7 Z. Fu, "Two characterizations of central BMO space via the commutators of Hardy operators" 33 (33): 505-529, 2021

      8 S. Lu, "The weighted Herz-type Hardy space and its applications" 38 (38): 662-673, 1995

      9 W. Guo, "The unified theory for the necessity of bounded commutators and applications" 30 (30): 3995-4035, 2020

      10 S. Lu, "The central BMO spaces and Littlewood–Paley operators" 11 (11): 72-94, 1995

      11 G. Hu, "The applications of weak Herz spaces" 26 (26): 417-428, 1997

      12 J. Alvarez, "Spaces of bounded λ-central mean oscillation, Morrey spaces, and λ-central Carleson measures" 51 (51): 1-47, 2000

      13 D. H. Wang, "Some new classes of BMO spaces" 60 (60): 833-846, 2017

      14 G. Gao, "Sharp weak estimates for Hardy-type operators" 7 (7): 421-433, 2016

      15 X. Nie, "Sharp constant of Hardy operators corresponding to general positive measures" 78-, 2018

      16 M. Wei, "Sharp bounds for Hardy-type operators on mixed radial-angular central Morrey spaces" 31-, 2023

      17 V. I. Burenkov, "Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. II" 4 (4): 21-45, 2013

      18 V. I. Burenkov, "Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. I" 3 (3): 11-32, 2012

      19 C. B. Morrey, "On the solutions of quasi-linear elliptic partial differential equations" 43 (43): 126-166, 1938

      20 B. I. Golubov, "On the boundedness of the Hardy and the Hardy–Littlewood operators in the spaces ReH1 and BMO" 188 (188): 1041-1054, 1997

      21 Y. Komori-Furuya, "Notes on commutators of Hardy operators" 7 (7): 329-334, 2003

      22 G. H. Hardy, "Note on a theorem of Hilbert" 6 (6): 314-317, 1920

      23 E. M. Stein, "Introduction to Fourier analysis on Euclidean spaces" Princeton Univ. Press 1971

      24 G. H. Hardy, "Inequalities" Cambridge Mathematical Library, Cambridge Univ. Press 1988

      25 Z. Fu, "Commutators of n-dimensional rough Hardy operators" 54 (54): 95-104, 2011

      26 S. Long, "Commutators of Hardy operators" 274 (274): 626-644, 2002

      27 D. H. Wang, "Characterizations of the BMO and Lipschitz spaces via commutators on weak Lebesgue and Morrey spaces" 39 (39): 583-590, 2023

      28 Qianjun He ; Mingquan Wei ; Dunyan Yan, "Characterizations of p-adic central Campanato spaces via commutator of p-adic Hardy type operators" 56 (56): 767-787, 2019

      29 C. Fefferman, "Characterizations of bounded mean oscillation" 77 : 587-588, 1971

      30 S. Shi, "Characterization of the central Campanato space via the commutator operator of Hardy type" 429 (429): 713-732, 2015

      31 Z. Fu, "Characterization for commutators of n-dimensional fractional Hardy operators" 50 (50): 1418-1426, 2007

      32 Z. Fu, "Cauchy-Szeg¨o commutators on weighted Morrey spaces" 296 (296): 1859-1885, 2023

      33 G. Gao, "Boundedness for commutators of n-dimensional rough Hardy operators on Morrey-Herz spaces" 64 (64): 544-549, 2012

      34 Z. Fu, "Boundedness for commutators of fractional Hardy operators in Herz spaces" 17 (17): 20-25, 2007

      35 R. Gong, "Boundedness and compactness of Cauchytype integral commutator on weighted Morrey spaces" 113 (113): 36-56, 2022

      36 M. Christ, "Best constants for two nonconvolution inequalities" 123 (123): 1687-1693, 1995

      37 F. Zhao, "A characterization of λ-central BMO space" 8 (8): 229-238, 2013

      38 L. Ji, "A characterization of the weak boundedness for commutators of Hardy-type operators on central Morrey spaces"

      39 M. Wei, "A characterization of CM O ⃗q via the commutator of Hardy-type operators on mixed Herz spaces" 101 (101): 5727-5742, 2022

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